Seminario de Geometría Algebraica

Seminario de Geometría Algebraica
2017-08-25
14:30-15:30hrs.
Mikhail Borovoi. Tel Aviv University
Tba
TBA
2017-03-31
14:30hrs.
José Ignacio Yáñez. PUC
Introducción al Minimal Model Program
Sala 2
Abstract:
Este semestre estudiaremos el Minimal Model Program (o teoría de Mori) para superficies algebraicas con borde. El objetivo principal es entender la demostración del teorema de boundedness dada por Alexeev a comienzos de los 90s. Este teorema implica que la compactificación del espacio de moduli de superficies algebraicas de tipo general, dada por Kollár y Shepherd-Barron y generalización de la compactificación de Deligne-Mumford para curvas, define una variedad proyectiva. En particular, las singularidades de las correspondientes superficies están acotadas a través de los números de Chern (de hecho  K^2 basta), formando una lista finita. ¿Cuál es esa lista para K^2 dado?

La idea es desarrollar todos los prerequicitos para poder entender los detalles de la demostración.

En esta charla se definirán superficies con bordes, las singularidades involucradas junto a sus discrepancias, el teorema del cono, y todo aspecto básico relacionado con MMP.
2017-03-24
14:30hrs.
Fabien Trihan. U Sophia, Japón
Abelian Varieties Over Function Fields And Related Conjecture
sala 2
Abstract:
We will talk about abelian varieties over function fields of positive characteristic and conjectures related to those such as the Birch-Swinnerton-Dyer, the equivariant Tamagawa number conjecture or the Iwasawa Main conjectures
2017-03-10
16:00hrs.
Dulip Piyaratne. Kavli Ipmu, University Of Tokyo
Stability Conditions On Derived Categories Of Varieties II
Sala 2
Abstract:
In this talk I will discuss stability conditions on projective threefolds. A conjectural construction for any 3-fold was introduced by Bayer, Macri and Toda, and the problem is reduced to proving so-called Bogomolov-Gieseker type inequality holds for certain stable objects in the derived category. It has been shown to hold for some 3-folds including Fano 3-folds of Picard rank one. However, Schmidt and Martinez gave some counter-examples for Fano 3-fold of higher Picard rank. In this talk, I will explain how to modify the original conjectural inequality in order to get a family of Bridgeland stability conditions, and why it holds for general Fano 3-folds.
2017-03-10
15:00hrs.
Dulip Piyaratne. Kavli Ipmu, University Of Tokyo
Stability Conditions On Derived Categories Of Varieties
Sala 2
Abstract:
The aim of this talk is to discuss Bridgeland stability conditions on smooth projective varieties. The notion of stability appears in many guises and it is fundamental to geometric invariant theory. There is a systematic way of studying stability conditions due to Bridgeland and his approach is essentially an abstraction of the usual slope stability for sheaves. This categorical stability notion was introduced in order to understand the work of Douglas on Pi-stability in superconformal field theories. However, construction of Bridgeland stability conditions on higher dimensional varieties is a challenging problem, and from string-theoretic point of view, stability conditions on smooth projective threefolds are the most interesting ones. In this talk, I will recall some important notions associated to derived categories of varieties and stability conditions, with special emphasis on curves and surfaces.
2016-12-01
16:15-17:15hrs.
Sukhendu Mehrotra. PUC Chile
The Franchetta Conjecture (Cont.)
Fac. de Matematicas, Universidad de Chile
2016-11-24
16:15-17:15hrs.
Sukhendu Mehrotra. Puc, Chile
The Franchetta Conjecture
Universidad de Chile
Abstract:
In 1952, Franchetta made the conjecture any line bundle over the universal curve defined over an open subset of M_g, g>2, restricts to the fibers as a multiple of the canonical bundle.
This talk will present a sketch of the proof of Arbarello-Cornalba of this conjecture.
2016-10-20
16:15-17:15hrs.
Anita Rojas. Universidad de Chile
Espacio de Teichmüller
Fac. de Matemáticas, Universidad de Chile
2016-10-13
16:15-17:15hrs.
Robert Auffarth. Universidad de Chile
M_G Como Espacio Analítico
Fac. de Matemáticas, U. de Chile
2016-10-06
16:15-17:15hrs.
Víctor González. Utfsm
Un Pincel de Curvas Estables
Fac. de Matemáticas, Universidad de Chile
2016-10-03
10:30hrs.
Cristián Ortiz. Universidad de Sao Paulo, Brasil
Vector Bundles Over Differentiable Stacks
Sala 2 (Edf. Rolando Chuaquí)
Abstract:
Stacks are generalized spaces arising in the study of moduli problems. In this seminar we will be mainly concerned with differentiable stacks. Roughly speaking, a differentiable stack is a generalized notion of quotient of a differentiable manifold, which includes orbifolds as special instances. There is a very fruitful interaction between differentiable stacks and the theory of Lie groupoids, namely, isomorphism classes of differentiable stacks are in one to one correspondence with Morita equivalence classes of Lie groupoids. In this talk, we will introduce the notion of Morita equivalence of vector bundles over Lie groupoids, we will explain in which sense this offers a notion of vector bundle in the category of differentiable stacks. Examples will be presented and, if time permits, we will briefly discuss connections with representation theory and symplectic geometry.
2016-09-29
16:15-17:15hrs.
Robert Auffarth. Universidad de Chile
Curvas Estables
Fac. de Mat., Universidad de Chile
2016-09-15
16:00hrs.
Sergio Troncoso. PUC Chile
Moduli y Esquemas de Hilbert (Cont.)
Fac. de Matemáticas, Universidad de Chile
Abstract:
Una indtroducción a los problemas de moduli y esquemas de Hilbert.
2016-09-09
11:00hrs.
Sergio Troncoso. PUC Chile
Moduli y Esquemas de Hilbert
Facultad de Matemáticas, Universidad de Chile
Abstract:
Una indtroducción a los problemas de moduli y esquemas de Hilbert.
2016-06-16
Giancarlo Urzúa. P. Universidad Católica de Chile
Degeneraciones de Superficies y Sus Modelos Minimales
Sala 2 de la Facultad de Matemáticas PUC a las 16:00 Hrs.
2016-05-06
Giancarlo Urzúa. P. Universidad Católica de Chile
Seminario Sobre Constantes de Seshadri: de Título: Cotas Para Constantes de Seshadri
Sala 2 de la Facultad de Matemáticas a las 14:30 Hrs.
2015-12-02
Bruno Suzuki. Universidad Católica del Norte
Cohomology Of Weighted Projective Spaces
Sala 1 - Facultad de Matemáticas UC
2015-06-26
Aníbal Velozo. Princeton University
Topología Simpléctica en Superficies Algebraicas y Horikawa Surfaces
Sala 2 Facultad de Matemáticas UC - 14:30 Hrs.
2015-06-19
Robert Auffart. Universidad de Chile
Sobre la Construcción de Mumford de Variedades Abelianas Degeneradas
Sala 2 Facultad de Matemáticas UC - 14:30 Hrs.
2015-03-27
Sebastián Eterovic. P. Universidad Católica de Chile
Buscando Curvas Racionales Cuando K es Negativo II
Sala 2 - Facultad de Matemáticas UC - 14:30