2020-06-22
11:30hrs.

Sergio Troncoso . UC Chile
Defensa de Tesis doctoral: "On the geography of surfaces of general type with fixed fundamental group"
Zoom (pedir a Ricardo Menares o Giancarlo Urzúa)
Abstract:

In this thesis, we study the geography of complex surfaces of general type with respect to the topological fundamental group. The understanding of this general problem can be coarsely divided into geographyof simply-connected surfaces and geography of non-simply-connected surfaces. 

The geography of simply-connected surfaces was intensively studied in the eighties and nineties by Persson, Chen, and Xiao among others. Due to their works, we know that the set of Chern slopes c^2_1/c_2 of simply-connected surfaces of general type is dense in the interval [1/5,2]. The last result which closes the density problem for this type of surfaces happened in 2015. Roulleau and Urz\'ua showed the density of the Chern slopes in the interval [1,3]. This completes the study since accumulation points of c^2_1/c_2 belong to the interval [1/5,3] by the Noether's inequality and the Bogomolov-Miyaoka-Yau inequality for complex surfaces. 

The geography of non-simply-connected surfaces is well understood only for small Chern slopes. Indeed, because of works of Mendes, Pardini, Reid, and Xiao, we know that for c_1^2/c_2 in [1/5, 1/3] the fundamental group is either finite with at most nine elements, or the fundamental (algebraic) group is commensurable with the fundamental (algebraic) group of a curve. Furthermore, a well-known conjecture of Reid states that for minimal surfaces of general type with c_1^2/c_2< 1/2 the topological fundamental group is either finite or it is commensurable with the fundamental group of a curve. Due to  Severi-Pardini's inequality and a theorem of Xiao,  Reid's conjecture is true, at least in the algebraic sense for irregular surfaces or surfaces having an irregular étale cover. Keum showed with an example in his doctoral thesis that Reid's conjecture cannot be extended over 1/2. 

For higher slopes essentially there are no general results. In this thesis, we prove that for any topological fundamental group G of a given nonsingular complex projective surface, the Chern slopes c ^2_1(S)/c_2(S) of minimal nonsingular projective surfaces of general type S with pi_1(S) isomorphic to G are dense in the interval [1, 3]. It remains open the question for non-simply-connected surfaces in the interval [1/2,1]. 

2020-06-16
13:00hrs.

Roberto Villaflor . Impa
How To Construct Hodge Cycles in Hypersurfaces?
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago

2020-06-09
13:00hrs.

Alexander Kuznetsov. Steklov Mathematical Institute
Gushel-Mukai Varieties
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
https://researchseminars.org/seminar/AG_Santiago

2020-05-26
13:00hrs.

Yulieth Prieto. Università Di Bologna
Automorfismos Simplécticos en Superficies K3
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
https://mathseminars.org/seminar/AG_Santiago

2020-05-19
13:00hrs.

José Ignacio Yáñez. U of Utah
Dimensión númerica de divisores
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
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.

Antonio Laface. U de Concepción
Cox Rings and Blowing-Ups
Zoom (pedir a Jenia Tevelev) visitar https://mathseminars.org/seminar/AG_Santiago
https://mathseminars.org/seminar/AG_Santiago

2020-05-05
14:00hrs.

Sebastian Torres. Umass Amherst
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.

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.

2019-11-26
14:00hrs.

Sebastián Torres . Umass - PUC
Windows Into Derived Categories of Git Quotients
sala 1

2019-11-19
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.

2019-11-12
14:00hrs.

Giancarlo Urzúa. PUC Chile
Construcción de Cho-Lee Después de Vial y Hacking
sala 1

2019-10-29
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.

2019-10-22
14:00hrs.

Giancarlo Urzúa. PUC Chile
Construcción de Cho-Lee Después de Vial y Hacking
sala 1

2019-10-15
14:00hrs.

Giancarlo Urzúa. PUC Chile
Colecciones Excepcionales en Superficies Simplemente Conexas de Género Cero
sala 1

2019-10-08
14:00hrs.

Pedro Montero. Utfsm
Categorías Derivadas de Ciertos Threefolds de Fano 2
sala 1

2019-10-01
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.

2019-09-24
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.

2019-09-10
14:00hrs.

Sergio Troncoso . PUC Chile
Categoría Derivada de Blow-Ups
sala 1

2019-09-05
14:15 - 15:05hrs.

Roberto Villaflor . Impa
Componentes del locus de Noether-Lefschetz superior
sala 1
Abstract:

2019-09-03
14:00hrs.

Sebastián Torres. Umass - PUC
Functores Derivados y Colecciones Excepcionales
sala 1