Seminario de Geometría Algebraica
Seminario de Geometría Algebraica
2020-06-09
13:00hrs.
13:00hrs.
Alexander Kuznetsov. Steklov Mathematical Institute
Gushel-Mukai Varieties
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https://researchseminars.org/seminar/AG_Santiago
Gushel-Mukai Varieties
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https://researchseminars.org/seminar/AG_Santiago
2020-05-26
13:00hrs.
13:00hrs.
Yulieth Prieto. Università Di Bologna
Automorfismos Simplécticos en Superficies K3
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https://mathseminars.org/seminar/AG_Santiago
Automorfismos Simplécticos en Superficies K3
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https://mathseminars.org/seminar/AG_Santiago
2020-05-19
13:00hrs.
13:00hrs.
José Ignacio Yáñez. U of Utah
Dimensión númerica de divisores
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Abstract:
https://mathseminars.org/seminar/AG_Santiago
Dimensión númerica de divisores
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Abstract:
Un invariante importante en el estudio de la geometría de un divisor es su dimensión de Iitaka. Ésta mide el crecimiento asintótico del espacio de secciones de los múltiplos del divisor. Sin embargo, la dimensión de Iitaka no se comporta bien en relación a la clase numérica del divisor, por lo que se han dado diversas definiciones que buscan capturar facetas de esta dimensión y que no dependan de la clase numérica.
En esta charla presentaré algunas definiciones de dimensión numérica de un divisor, junto con un ejemplo que evidencia problemas con estas definiciones y preguntas que surgen a partir de esto.
https://mathseminars.org/seminar/AG_Santiago
2020-05-12
14:00hrs.
14:00hrs.
Antonio Laface. U de Concepción
Cox Rings and Blowing-Ups
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https://mathseminars.org/seminar/AG_Santiago
Cox Rings and Blowing-Ups
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https://mathseminars.org/seminar/AG_Santiago
2020-05-05
14:00hrs.
14:00hrs.
Sebastian Torres. Umass Amherst
Bott Desaparición Via Git y Cuantización
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https://mathseminars.org/seminar/AG_Santiago
Bott Desaparición Via Git y Cuantización
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
https://mathseminars.org/seminar/AG_Santiago
2020-01-08
14:00hrs.
14:00hrs.
Luca Schaffler. University of Massachusetts At Amherst
Compactifications of moduli spaces of algebraic varieties
sala 2
Abstract:
In algebraic geometry, an algebraic variety is a geometric object defined
by polynomial equations. The space of parameters for a family of algebraic
varieties may also be an algebraic variety called a moduli space. In this
talk oriented to a general audience, I will motivate the study of
compactifications of moduli spaces, focusing on the case of moduli of
polarized K3 surfaces. The original results (joint works with Moon and
Gallardo-Kerr) concern the study of a family of K3 surfaces arising from
eight points in the projective line, and the interplay between different
compactifications of such family coming from Geometric Invariant Theory,
Hodge Theory, and the Minimal Model Program.
Compactifications of moduli spaces of algebraic varieties
sala 2
Abstract:
In algebraic geometry, an algebraic variety is a geometric object defined
by polynomial equations. The space of parameters for a family of algebraic
varieties may also be an algebraic variety called a moduli space. In this
talk oriented to a general audience, I will motivate the study of
compactifications of moduli spaces, focusing on the case of moduli of
polarized K3 surfaces. The original results (joint works with Moon and
Gallardo-Kerr) concern the study of a family of K3 surfaces arising from
eight points in the projective line, and the interplay between different
compactifications of such family coming from Geometric Invariant Theory,
Hodge Theory, and the Minimal Model Program.
2019-11-26
14:00hrs.
14:00hrs.
Sebastián Torres . Umass - PUC
Windows Into Derived Categories of Git Quotients
sala 1
Windows Into Derived Categories of Git Quotients
sala 1
2019-11-19
14:00hrs.
14:00hrs.
Jenia Tevelev. Umass - PUC
Quotient stacks and their derived categories
sala 1
Abstract:
We will introduce the notion of an algebraic stack, a generalization of an algebraic variety. We will discuss vector bundles, coherent sheaves and derived categories of algebraic stacks, focusing in simple examples of quotient stacks.
Quotient stacks and their derived categories
sala 1
Abstract:
We will introduce the notion of an algebraic stack, a generalization of an algebraic variety. We will discuss vector bundles, coherent sheaves and derived categories of algebraic stacks, focusing in simple examples of quotient stacks.
2019-11-12
14:00hrs.
14:00hrs.
2019-10-29
14:00hrs.
14:00hrs.
Ana-María Castravet. Université de Versailles
Moduli spaces of stable rational curves with marked points
sala 1
Abstract:
We will discuss Hassett's construction of moduli spaces of weighted stable rational curves with marked points. We will explain how different choices of weights at the points lead to different stability conditions and how the various moduli spaces are related by blow-ups and blow-downs. In particular, one can recover Kapranov's description of the Grothendieck-Knudsen moduli spaces, or the Losev-Manin moduli spaces, as iterated blow-ups of projective spaces. Furthermore, I will discuss how Hassett spaces appear naturally as GIT quotients or their desingularizations. If time permits, we will discuss exceptional collections on some of these spaces.
Moduli spaces of stable rational curves with marked points
sala 1
Abstract:
We will discuss Hassett's construction of moduli spaces of weighted stable rational curves with marked points. We will explain how different choices of weights at the points lead to different stability conditions and how the various moduli spaces are related by blow-ups and blow-downs. In particular, one can recover Kapranov's description of the Grothendieck-Knudsen moduli spaces, or the Losev-Manin moduli spaces, as iterated blow-ups of projective spaces. Furthermore, I will discuss how Hassett spaces appear naturally as GIT quotients or their desingularizations. If time permits, we will discuss exceptional collections on some of these spaces.
2019-10-22
14:00hrs.
14:00hrs.
Giancarlo Urzúa. PUC Chile
Construcción de Cho-Lee Después de Vial y Hacking
sala 1
Construcción de Cho-Lee Después de Vial y Hacking
sala 1
2019-10-15
14:00hrs.
14:00hrs.
Giancarlo Urzúa. PUC Chile
Colecciones Excepcionales en Superficies Simplemente Conexas de Género Cero
sala 1
Colecciones Excepcionales en Superficies Simplemente Conexas de Género Cero
sala 1
2019-10-08
14:00hrs.
14:00hrs.
2019-10-01
14:00hrs.
14:00hrs.
Pedro Montero. Utfsm
Categorías derivadas de ciertos threefolds de Fano
sala 1
Abstract:
En esta charla discutiremos sobre las categorías derivadas de ciertos ejemplos explícitos de variedades de Fano de dimensión 3. Discutiremos la conexión con el problema de racionalidad de dichas variedades, siguiendo la filosofía de Kuznetsov que afirma que la racionalidad debe verse reflejada de manera geométrica dentro de la categoría derivada.
Categorías derivadas de ciertos threefolds de Fano
sala 1
Abstract:
En esta charla discutiremos sobre las categorías derivadas de ciertos ejemplos explícitos de variedades de Fano de dimensión 3. Discutiremos la conexión con el problema de racionalidad de dichas variedades, siguiendo la filosofía de Kuznetsov que afirma que la racionalidad debe verse reflejada de manera geométrica dentro de la categoría derivada.
2019-09-24
14:00hrs.
14:00hrs.
Jenia Tevelev. Umass - PUC
Mutations in derived category
sala 1
Abstract:
I will discuss mutations in derived category with an emphasis on del Pezzo surfaces. Time permitting, I will sketch a proof of the famous theorem of Rudakov that exceptional collections of vector bundles on the projective plane correspond to solutions of the Markov equation x^2+y^2+z^2=3xyz.
Mutations in derived category
sala 1
Abstract:
I will discuss mutations in derived category with an emphasis on del Pezzo surfaces. Time permitting, I will sketch a proof of the famous theorem of Rudakov that exceptional collections of vector bundles on the projective plane correspond to solutions of the Markov equation x^2+y^2+z^2=3xyz.
2019-09-10
14:00hrs.
14:00hrs.
Sergio Troncoso . PUC Chile
Categoría Derivada de Blow-Ups
sala 1
Categoría Derivada de Blow-Ups
sala 1
2019-09-05
14:15 - 15:05hrs.
14:15 - 15:05hrs.
Roberto Villaflor . Impa
Componentes del locus de Noether-Lefschetz superior
sala 1
Abstract:
Componentes del locus de Noether-Lefschetz superior
sala 1
Abstract:
El locus de Noether-Lefschetz corresponde al espacio de parámetros de superficies en P3 con número de Picard mayor que 1. Este espacio fué intensamente estudiado a principios de los 90 por M. Green, C. Voisin, J. Harris entre otros, como consequencia del desarrollo de las variaciones infinitesimales de estrucutras de Hodge liderado por P. Griffiths. En esta charla expositoria hablaremos de los resultados conocidos sobre el locus de Noether-Lefschetz, e introduciremos el espacio análogo para hipersuperficies de dimension superior, el llamado locus de Hodge. Si el tiempo lo permite, mencionaremos cómo ciertos resultados sobre el locus de Noether-Lefschetz se generalizan para el locus de Hodge.
2019-09-03
14:00hrs.
14:00hrs.
Sebastián Torres. Umass - PUC
Functores Derivados y Colecciones Excepcionales
sala 1
Functores Derivados y Colecciones Excepcionales
sala 1
2019-08-27
14:00hrs.
14:00hrs.
Sebastián Torres. Umass Amherst - PUC Chile
Definition of Derived Category
sala 1
Definition of Derived Category
sala 1
2019-08-20
14:00hrs.
14:00hrs.
Jenia Tevelev. Umass Amherst - PUC Chile
Introducción a la Geometría de Las Categorías Derivadas 2
sala 1
Introducción a la Geometría de Las Categorías Derivadas 2
sala 1
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