Seminario de Geometría Algebraica
Seminario de Geometría Algebraica13:30hrs.
Baby: Mini Introducción a Geometría Birracional
sala 2
13:30hrs.
Vector Bundles in Projective Spaces
sala 2
13:30hrs.
Baby: Mmp y Curvas Racionales Con Grado Arbitrariamente Alto en Superficies K3
sala 2
13:30hrs.
Transitioning to higher dimensions
sala 2
Abstract:
What is currently known? What are the main obstructions? Lagrangian fibrations in IHS varieties.
13:30hrs.
Elliptic fibrations on K3 surfaces
sala 2
Abstract:
Invariants of elliptic fibrations on K3 surfaces. Applications of Torelli Theorem for the moduli of K3 surfaces admitting elliptic fibrations. Lattice-based criteria for the existence of elliptic fibrations. The Shioda formula.
13:30hrs.
Baby: Superficies de Tipo General a Partir de Superficies K3 y Curvas Racionales
sala 2
13:30hrs.
The bilinear form of the second cohomology group and the Néron-Severi lattice
sala 2
Abstract:
Basic definition of lattices. The discriminant group. The bilinear form associated with the cohomology of a K3 surface and the abstract K3 lattice. The problem of existence, uniqueness, and embedding of lattices. The Beauville-Bogomolov form for IHS manifolds.
13:30hrs.
Baby: Deformaciones de Superficies Algebraicas y Obstrucciones
sala 2
13:30hrs.
Automorphism Groups and Quotients
sala 2
Abstract:
Symplectic and non-symplectic. General properties of these automorphisms. Quotients of K3 surfaces by automorphisms of finite order. Applications of Torelli Theorem. Comments on the automorphism group for the Hilbert scheme of points on K3 surfaces.
https://sites.google.com/view/yuliethprietom/teaching/seminario-puc?authuser=0
13:30hrs.
Baby: Superficies Singulares y No Singulares
sala 2
13:30hrs.
Teorema de Torelli para superficies K3
sala 2
Abstract:
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Torelli Theorem for K3 surfaces and its proof. Period map. Moduli of polarized K3 surfaces (the case of Kummer surfaces). Formulation of Torelli Theorem for IHS manifolds.
13:30hrs.
Baby: Fracciones Continuas Negativas, Cadenas de Wahl, Fracciones del 0
sala 2
13:30hrs.
K3 surfaces: definiciones y problemas
sala 2
Abstract:
The goal of this seminar is to present the fundamental tools for formulating questions related to the study of specific geometric properties of K3 surfaces (e.g., such as automorphisms, elliptic fibrations, Shioda-Inose structures). Furthermore, it aims to explore the analogue of these tools in the context of higher-dimensional varieties, known as irreducible holomorphic symplectic (IHS) manifolds or Hyperkähler.
https://sites.google.com/view/yuliethprietom/teaching/seminario-puc?authuser=0
13:30hrs.
BABY: Fracciones continuas negativas en geometría birracional
sala 2
Abstract:
Será una introducción a geometría birracional de degeneraciones de superficies complejas, basado en el libro en progreso "Negative continued fractions in birational geometry: A guide to Wahl degenerations of surfaces".
Tópicos guías:
1. Hirzebruch-Jung continued fractions
1.1. Basics
1.2. Wahl chains
1.3. Zero continued fractions
2. Singular and nonsingular algebraic surfaces
2.1. Generalities on surfaces and singularities
2.2. Cyclic quotient singularities
2.3. T-singularities
3. Deformations
3.1. General basic theory for affine and proper varieties
3.2. Q-Gorenstein deformations
3.3. Kollár–Shepherd-Barron correspondence
4. W-surfaces
4.1. Picard group, class group, and topology
4.2. MMP for W-surfaces I
4.3. MMP for W-surfaces II
5. N-resolutions
5.1. Existence and uniqueness
5.2. Braid group action
6. Exceptional collections of Hacking bundles
6.1. Hacking exceptional bundles
6.2. Hacking exceptional collections
6.3. Exceptional collections and H.e.c.s
13:30hrs.
Deformations of the Kalck-Karmazyn Algebra via Homological Mirror Symmetry
sala 2
Abstract:
Kawamata observed that a Q-Gorenstein smoothing of a Wahl singularity gives rise to a matrix order, i.e., a 1-parameter flat degeneration of a matrix algebra. Tevelev and Urzúa later generalized this result to general smoothings of 2-dimensional cyclic quotient singularities. However, these results were proved using abstract methods of birational geometry, making explicit calculations challenging. In joint work with Yanki Lekili, we use homological mirror symmetry to derive explicit formulas for Kawamata’s matrix orders.
13:30hrs.
Grand Finale: Superficies de K3 y Condiciones de Estabilidad
sala 2
13:30hrs.
Fano visitor conjecture for K3 surfaces
sala 2
Abstract:
13:30hrs.
Baby Baby: Cocientes de Variedades Afines Por Grupos Finitos
sala 2
13:30hrs.
Geometría Birracional de Espacios de Moduli
sala 2
13:30hrs.
Baby Baby: Transformaciones de Cremona
sala 2