research - Nicolás Botbol's Homepage -
Area of interest: Commutative Algebra, Algebraic Geometry and Homological Algebra. In particular, I realy like homological algebra in elimination theory, Castelnuovo-Mumford regularity.
Permanent research position. Assistant Researcher at CONICET, Buenos Aires, Argentina.
Title: Homological aspects of commutative graded rings and applications to algebraic geometry.
Researcher in charge: Alicia Dickenstein
Postdoctoral position. Marie Curie Postdoctoral Fellowships - INRIA, Sophia Anripolis.
Title: Matrix-based representations of rational hypersurfaces.
Advisors: Laurent Busé (INRIA)
Postdoctoral position. Postdoctoral Fellowships from CONICET.
Title: Homological aspects of commutative graded rings.
Advisors: Alicia Dickenstein (UBA) & Aldo Conca (U. Genova).
PhD. from the University of Buenos Aires & the University of Pierre et Marie Curie, Paris 6. Sep 2010.
Title: Implicitization of rational maps.
Advisors: Marc Chardin (UPMC). & Alicia Dickenstein (UBA)
Graduate Studies from the University of Buenos Aires. Feb 2007.
Title: Implicitación de hipersuperficies racionales mediante complejos de aproximación.
Advisor: Alicia Dickenstein (UBA).
_____________________________________________________________________________________________________________
Published / accepted articles:
[8] (with A. Dickenstein) Implicitization of rational hypersurfaces via linear syzygies: a practical overview. arXiv:1502.00890. To apperar in Journal of Symbolic Computation (2015).
[7] (with M. Chardin) Castelnuovo Mumford Regularity with respect to multigraded ideals. arXiv:1107.2494v2. To apperar in Journal of Algebra (2015).
[6] (with L. Busé and M. Chardin) Fitting ideals and multiple-points of surface parameterizations. arXiv:1310.4915 . Journal of Algebra. Vol 420, Issue 1 (2014), 486-508.
[5] The implicit equation of a multigraded hypersurface. arXiv:1007.3437v3 . Journal of Algebra. Vol 348, Issue 1 (2011), 381-401.
[4] Compactifications of rational maps and the implicit equations of their images. arXiv:0910.1340v2. Journal of Pure and Applied Algebra. Vol 215, Issue 5 (2011), 1053-1068.
[3] (with A. Dickenstein and M. Dohm) Matrix representations for toric parametrizations. arXiv:0807.4802. Computer Aided Geometric Design. Vol 26, Issue 7 (2009), 757-771.
[2] The implicitization problem for $\phi: P^n --> (P^1)^{n+1}$. arXiv:0803.0573v2. Journal of Algebra. Vol 322, Issue 11 (2009), 3878-3895.
[1] Mini-Workshop: Surface Modeling and Syzygies, Mathematisches Forschungsinstitut Oberwolfach. European Math. Soc., Oberwolfach Report No. 54/2007, (Proceeding) pp. 3189.
Preprints:
[2] (with M. Dohm and M. Dubinsky) A package for computing implicit equations of parametrizations from toric surfaces. arXiv:1001.1126. January 2010.
[1] An algorithm for computing implicit equations of bigraded rational surfaces. arXiv:1007.3690 . July 2010.
My publications in arXiv and MathSciNet.
Lecture Notes:
[1] Introducción a la Teoría de Eliminación. Lecture Notes. FAMAF, UNC. Serie "B" Vol 63 (2012), 89-126.
Talks in congresses:
[13] IV Congreso Latinoamericano de Matemáticos - 6th to 10th August 2012 - Córdoba, Argentina.
Invited talk: Castelnuovo Mumford Regularity with respect to multigraded ideals.
[12] Encuentro Nacional de Álgebra VI - 2nd to 4th August 2012 - La Falda, Córdoba, Argentina.
Course: Introducción a la Teoría de Eliminación.
[11] The SAGA-ΕρΓΑ-GALAAD meeting - 9th to 10th January 2012, Athens, Greece.
Short communication: What is a "good" definition for the image of a map of schemes?
[10] ELGA : First Latinamerican School of Algebraic Geometry and Aplications - 8th to 12th August 2011 - La Cumbre, Córdoba, Argentina.
Invited talk: Implicit equations of rational hypersurfaces via free resolutions..
[9] Saga 2010: Fall School Shapes, Geometry, and Algebra - 3rd to 8th October 2010 - Kolympari, Crete, Greece.
Poster: Implicit equations of bigraded surfaces.
[8] XIX Encuentro Rioplatense de Álgebra y Geometría Algebraica - 19 al 21 de Noviembre de 2009 - Montevideo, Uruguay.
Invited talk: Ecuaciones implícitas de aplicaciones racionales multigraduadas.
[7] Unión de Matemática Argentina 2009: Sesión de Algebra - 24th september 2009 - Cdad. de Mendoza, Argentina.
Invited talk: Multigraded Castelnuovo-Mumford regulity and applications.
[6] PASI 2009: Pan-American Advanced Study Institute, in Commutative Algebra and its Connections to Geometry, honoring Wolmer Vasconcelos - 3rd to 14th August 2009 - Olinda, Brazil.
Invited talk: Implicit equations of multigraded hypersurfaces.
[5] MEGA'09: Effective Methods in Algebraic Geometry - 15th to 19th june 2009 - Barcelona, Spain.
Invited talk: Compactifications for the matrix representation problem.
[4] Unión de Matemática Argentina 2008: Sesión de Algebra - 24th to 27th september 2008 - Cdad. de Mendoza, Argentina.
Short communication: Implicitación de superficies con parametrizaciones tóricas.
[3] Conferencia Internacional sobre Algebra Conmutativa, Combinatoria y Computacional en Honor de Pilar Pisón Casares - 11th to 16th february 2008 - Universidad Autónoma de Sevilla, Sevilla, Spain.
Poster: Implicitization of rational hypersurfaces in a product of unidimensional projective spaces.
[2] Mini-Workshop on Surface Modeling and Syzygies - 25 november to 1st december 2007 - Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany;
Invited talk: Implicitization of rational hypersurfaces for the case φ : P^n --> (P^1)^{n+1}.
[1] Unión de Matemática Argentina 2007: Sesión de Algebra - 17th to 22nd september 2007 - Cdad. de Córdoba, Argentina;
Short communication: Implicitación de hipersuperficies racionales en productos de espacios proyectivos unidimensionales
Talks in Seminars:
[13] Seminario de álgebra homológica - 6th and 13th july 2012 - FCEN-UBA, Buenos Aires Argentina;
Title of the talk: Métodos homológicos en teoría de eliminación.
[12] Séminaire du Groupe GALAAD (INRIA) - 11th october 2011 - INRIA, Sophia-Antipolis, France;
Title of the talk: Autour de la régularité de Castelnuovo-Mumford.
[11] Seminario d'algebra e geometria - 22nd june 2011 - DIMA, Genova, Italy;
Title of the talk: Implicit equations of rational hypersurfaces via free resolutions.
[10] Seminario d'algebra commutativa - 1st june 2011 - DIMA, Genova, Italy;
Title of the talk: Homological algebra in elimination theory.
[9] Séminaire du Groupe GALAAD (INRIA) - 8th june 2009 - INRIA, Sophia-Antipolis, France;
Title of the talk: Rational maps with image in (P^1)^n.
[8] Seminario de Geometría Algebraica de Universidad de Valladolid - 12th february 2009 - Universidad de Valladolid, Valladolid, Spain;
Title of the talk: Métodos de eliminación para la implicitación en diversos contextos.
[7] Two talks at IMJ - 3rd and 10th february 2009 - (IMJ) Institut de mathématiques de Jussieu, Paris, France;
Title of the talks: Images of rational maps I & II.
[6] Séminaire du Groupe GALAAD (INRIA) - 10th october 2008 - INRIA, Sophia-Antipolis, France;
Title of the talk: Représentations matricielles pour des paramétrisations toriques.
[5] Seminario de Geometría Algebraica de Università de Barcelona - 8th february 2008 - Università de Barcelona, Barcelona, Spain;
Title of the talk: Implicitación de hypersuperficies racionales en productos en el caso φ : Pn --> (P^1)^{n+1}.
[4] Séminaire du Groupe GALAAD (INRIA) - 23rd may 2007 - INRIA, Sophia-Antipolis, France;
Title of the talk: Calcul de discriminants au moyen des complexes d’approximation.
[3] Seminario de Geometría Algebraica y Aplicaciones - FCEyN, UBA, Buenos Aires, Argentina;
several talks, cf. the website of the seminar: http://cms.dm.uba.ar/actividades/seminarios/geometria_algebraica_y_aplicaciones/index.html
[2] Seminario de Geometría Algebraica - FCEyN, UBA, Buenos Aires, Argentina;
several talks, cf. the website of the seminar: http://mate.dm.uba.ar/ fcukier/SGA
[1] Seminario de alumnos de doctorado - FCEyN, UBA, Buenos Aires, Argentina.
Software implementations:
[4] (with L. Busé and M. Dubinsky) Macaulay2 code for elimination theory, in particular, for resultants computations:
* Download code for Macaulay 1.4. May 2012.
* html Macaulay2 documentation.
* pdf introductory file.
The last version can be downloaded from the "resultants-macaulay2" google project. Use this command to anonymously check out the latest project source code:
svn checkout http://resultants-macaulay2.googlecode.com/svn/ resultants-macaulay2-read-only
[3] Macaulay2 code for computing the implicit equation of a bigraded surface in P^3 without embedding:
* Download code for Macaulay 1.4. May 2011.
* html Macaulay2 documentation.
* pdf introductory file.
[2] (with M. Dohm and M. Dubinsky) Further improovements in the implementation on Macaulay2 for computing the implicit equation of a toric surface in P^3. Several versions:
* Download code for Macaulay 1.4. January 2012.
* html Macaulay2 documentation.
* pdf introductory file.
Download code for Macaulay 1.3.1 or older. January 2011.
Download code for Macaulay 1.3.1 or older (old version of the code). July 2010.
Exercises porposed for SAGA, Kolympari, Crete, Greece, 2010: SAGAexerciseM2.txt
[1] (with A. Dickenstein and M. Dohm) Apendix for "Matrix representations for toric parametrizations. CGAD". Implementation on Macaulay2 for computing the implicit equation of a toric surface in P^3. Requires 'maxminor.m2'. Download PDF file and code. August 2008.
PhD. Thesis:
Implicitization of rational maps. University of Buenos Aires & the University of Pierre et Marie Curie, Paris 6. 29th September 2010. Advisors: Alicia Dickenstein (UBA) & Marc Chardin (UPMC). arXiv:1109.1423.
Degree Thesis:
Implicitación de hipersuperficies racionales mediante complejos de aproximación. FCEyN, Universidad de Buenos Aires. 12th february 2007. Advisor: Alicia Dickenstein.
Area of interest: Commutative Algebra, Algebraic Geometry and Homological Algebra. In particular, I realy like homological algebra in elimination theory, Castelnuovo-Mumford regularity.
Title: Homological aspects of commutative graded rings and applications to algebraic geometry.
Researcher in charge: Alicia Dickenstein
Title: Matrix-based representations of rational hypersurfaces.
Advisors: Laurent Busé (INRIA)
Title: Homological aspects of commutative graded rings.
Advisors: Alicia Dickenstein (UBA) & Aldo Conca (U. Genova).
PhD. from the University of Buenos Aires & the University of Pierre et Marie Curie, Paris 6. Sep 2010.
Title: Implicitization of rational maps.
Advisors: Marc Chardin (UPMC). & Alicia Dickenstein (UBA)
Graduate Studies from the University of Buenos Aires. Feb 2007.
Title: Implicitación de hipersuperficies racionales mediante complejos de aproximación.
Advisor: Alicia Dickenstein (UBA). _____________________________________________________________________________________________________________
Published / accepted articles:
[8] (with A. Dickenstein) Implicitization of rational hypersurfaces via linear syzygies: a practical overview. arXiv:1502.00890. To apperar in Journal of Symbolic Computation (2015).
[7] (with M. Chardin) Castelnuovo Mumford Regularity with respect to multigraded ideals. arXiv:1107.2494v2. To apperar in Journal of Algebra (2015).
[6] (with L. Busé and M. Chardin) Fitting ideals and multiple-points of surface parameterizations. arXiv:1310.4915 . Journal of Algebra. Vol 420, Issue 1 (2014), 486-508.
[5] The implicit equation of a multigraded hypersurface. arXiv:1007.3437v3 . Journal of Algebra. Vol 348, Issue 1 (2011), 381-401.
[4] Compactifications of rational maps and the implicit equations of their images. arXiv:0910.1340v2. Journal of Pure and Applied Algebra. Vol 215, Issue 5 (2011), 1053-1068.
[3] (with A. Dickenstein and M. Dohm) Matrix representations for toric parametrizations. arXiv:0807.4802. Computer Aided Geometric Design. Vol 26, Issue 7 (2009), 757-771.
[2] The implicitization problem for $\phi: P^n --> (P^1)^{n+1}$. arXiv:0803.0573v2. Journal of Algebra. Vol 322, Issue 11 (2009), 3878-3895.
[1] Mini-Workshop: Surface Modeling and Syzygies, Mathematisches Forschungsinstitut Oberwolfach. European Math. Soc., Oberwolfach Report No. 54/2007, (Proceeding) pp. 3189.
Preprints:
[2] (with M. Dohm and M. Dubinsky) A package for computing implicit equations of parametrizations from toric surfaces. arXiv:1001.1126. January 2010.
[1] An algorithm for computing implicit equations of bigraded rational surfaces. arXiv:1007.3690 . July 2010.
My publications in arXiv and MathSciNet.
Lecture Notes:
[1] Introducción a la Teoría de Eliminación. Lecture Notes. FAMAF, UNC. Serie "B" Vol 63 (2012), 89-126.
Talks in congresses:
[13] IV Congreso Latinoamericano de Matemáticos - 6th to 10th August 2012 - Córdoba, Argentina.
Invited talk: Castelnuovo Mumford Regularity with respect to multigraded ideals.
[12] Encuentro Nacional de Álgebra VI - 2nd to 4th August 2012 - La Falda, Córdoba, Argentina.
Course: Introducción a la Teoría de Eliminación.
[11] The SAGA-ΕρΓΑ-GALAAD meeting - 9th to 10th January 2012, Athens, Greece.
Short communication: What is a "good" definition for the image of a map of schemes?
[10] ELGA : First Latinamerican School of Algebraic Geometry and Aplications - 8th to 12th August 2011 - La Cumbre, Córdoba, Argentina.
Invited talk: Implicit equations of rational hypersurfaces via free resolutions..
[9] Saga 2010: Fall School Shapes, Geometry, and Algebra - 3rd to 8th October 2010 - Kolympari, Crete, Greece.
Poster: Implicit equations of bigraded surfaces.
[8] XIX Encuentro Rioplatense de Álgebra y Geometría Algebraica - 19 al 21 de Noviembre de 2009 - Montevideo, Uruguay.
Invited talk: Ecuaciones implícitas de aplicaciones racionales multigraduadas.
[7] Unión de Matemática Argentina 2009: Sesión de Algebra - 24th september 2009 - Cdad. de Mendoza, Argentina.
Invited talk: Multigraded Castelnuovo-Mumford regulity and applications.
[6] PASI 2009: Pan-American Advanced Study Institute, in Commutative Algebra and its Connections to Geometry, honoring Wolmer Vasconcelos - 3rd to 14th August 2009 - Olinda, Brazil.
Invited talk: Implicit equations of multigraded hypersurfaces.
[5] MEGA'09: Effective Methods in Algebraic Geometry - 15th to 19th june 2009 - Barcelona, Spain.
Invited talk: Compactifications for the matrix representation problem.
[4] Unión de Matemática Argentina 2008: Sesión de Algebra - 24th to 27th september 2008 - Cdad. de Mendoza, Argentina.
Short communication: Implicitación de superficies con parametrizaciones tóricas.
[3] Conferencia Internacional sobre Algebra Conmutativa, Combinatoria y Computacional en Honor de Pilar Pisón Casares - 11th to 16th february 2008 - Universidad Autónoma de Sevilla, Sevilla, Spain.
Poster: Implicitization of rational hypersurfaces in a product of unidimensional projective spaces.
[2] Mini-Workshop on Surface Modeling and Syzygies - 25 november to 1st december 2007 - Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany;
Invited talk: Implicitization of rational hypersurfaces for the case φ : P^n --> (P^1)^{n+1}.
[1] Unión de Matemática Argentina 2007: Sesión de Algebra - 17th to 22nd september 2007 - Cdad. de Córdoba, Argentina;
Short communication: Implicitación de hipersuperficies racionales en productos de espacios proyectivos unidimensionales
Talks in Seminars:
[13] Seminario de álgebra homológica - 6th and 13th july 2012 - FCEN-UBA, Buenos Aires Argentina;
Title of the talk: Métodos homológicos en teoría de eliminación.
[12] Séminaire du Groupe GALAAD (INRIA) - 11th october 2011 - INRIA, Sophia-Antipolis, France;
Title of the talk: Autour de la régularité de Castelnuovo-Mumford.
[11] Seminario d'algebra e geometria - 22nd june 2011 - DIMA, Genova, Italy;
Title of the talk: Implicit equations of rational hypersurfaces via free resolutions.
[10] Seminario d'algebra commutativa - 1st june 2011 - DIMA, Genova, Italy;
Title of the talk: Homological algebra in elimination theory.
[9] Séminaire du Groupe GALAAD (INRIA) - 8th june 2009 - INRIA, Sophia-Antipolis, France;
Title of the talk: Rational maps with image in (P^1)^n.
[8] Seminario de Geometría Algebraica de Universidad de Valladolid - 12th february 2009 - Universidad de Valladolid, Valladolid, Spain;
Title of the talk: Métodos de eliminación para la implicitación en diversos contextos.
[7] Two talks at IMJ - 3rd and 10th february 2009 - (IMJ) Institut de mathématiques de Jussieu, Paris, France;
Title of the talks: Images of rational maps I & II.
[6] Séminaire du Groupe GALAAD (INRIA) - 10th october 2008 - INRIA, Sophia-Antipolis, France;
Title of the talk: Représentations matricielles pour des paramétrisations toriques.
[5] Seminario de Geometría Algebraica de Università de Barcelona - 8th february 2008 - Università de Barcelona, Barcelona, Spain;
Title of the talk: Implicitación de hypersuperficies racionales en productos en el caso φ : Pn --> (P^1)^{n+1}.
[4] Séminaire du Groupe GALAAD (INRIA) - 23rd may 2007 - INRIA, Sophia-Antipolis, France;
Title of the talk: Calcul de discriminants au moyen des complexes d’approximation.
[3] Seminario de Geometría Algebraica y Aplicaciones - FCEyN, UBA, Buenos Aires, Argentina;
several talks, cf. the website of the seminar: http://cms.dm.uba.ar/actividades/seminarios/geometria_algebraica_y_aplicaciones/index.html
[2] Seminario de Geometría Algebraica - FCEyN, UBA, Buenos Aires, Argentina;
several talks, cf. the website of the seminar: http://mate.dm.uba.ar/ fcukier/SGA
[1] Seminario de alumnos de doctorado - FCEyN, UBA, Buenos Aires, Argentina.
Software implementations:
[4] (with L. Busé and M. Dubinsky) Macaulay2 code for elimination theory, in particular, for resultants computations:
* Download code for Macaulay 1.4. May 2012.
* html Macaulay2 documentation.
* pdf introductory file.
The last version can be downloaded from the "resultants-macaulay2" google project. Use this command to anonymously check out the latest project source code:
svn checkout http://resultants-macaulay2.googlecode.com/svn/ resultants-macaulay2-read-only
[3] Macaulay2 code for computing the implicit equation of a bigraded surface in P^3 without embedding:
* Download code for Macaulay 1.4. May 2011.
* html Macaulay2 documentation.
* pdf introductory file.
[2] (with M. Dohm and M. Dubinsky) Further improovements in the implementation on Macaulay2 for computing the implicit equation of a toric surface in P^3. Several versions:
* Download code for Macaulay 1.4. January 2012.
* html Macaulay2 documentation.
* pdf introductory file.
Download code for Macaulay 1.3.1 or older. January 2011.
Download code for Macaulay 1.3.1 or older (old version of the code). July 2010.
Exercises porposed for SAGA, Kolympari, Crete, Greece, 2010: SAGAexerciseM2.txt
[1] (with A. Dickenstein and M. Dohm) Apendix for "Matrix representations for toric parametrizations. CGAD". Implementation on Macaulay2 for computing the implicit equation of a toric surface in P^3. Requires 'maxminor.m2'. Download PDF file and code. August 2008.
PhD. Thesis:
Implicitization of rational maps. University of Buenos Aires & the University of Pierre et Marie Curie, Paris 6. 29th September 2010. Advisors: Alicia Dickenstein (UBA) & Marc Chardin (UPMC). arXiv:1109.1423.
Degree Thesis:
Implicitación de hipersuperficies racionales mediante complejos de aproximación. FCEyN, Universidad de Buenos Aires. 12th february 2007. Advisor: Alicia Dickenstein.