PoS-EC
Postdoc Seminar of the Erdős Center
Postdoc Seminar of the Erdős Center
Welcome to the PoS-EC webpage!
PoS-EC is a seminar organized by the postdocs of the Erdős Center coming for the Simons Semester in Algebraic Geometry. The purpose of this seminar is to share our research with the Alfréd Rényi Institute community, and public in general. We might have external invited speakers in the future.
Place: Seminar Room of the Erdős Center (Google maps).
Contact: leal [at] renyi [dot] hu
UPCOMING TALKS
September 30, 14:00
Speaker: Andrei Stoenică
Title: Hilbert schemes and Brill-Noether theory
Abstract: The first part of this talk serves as an overview of the theory of Hilbert schemes, Brill-Noether theory and subvarieties of M_g, the moduli space of genus g curves, which parametrize degree d covers of fixed genus curves. These subvarieties include the ones given by Brill-Noether conditions related to linear series of g^1_d type and generalize them in a way, as the previously mentioned covering conditions go beyond the scope of classical Brill-Noether theory. The second part focuses on some recent work on the geometry of said loci in the case of subvarieties parametrizing covers of genus 1 curves and how Hilbert schemes can be used in order to analyze them.
PAST TALKS
September 9, 13:00
Speaker: Nikolaos Tsakanikas
Title: Singular symplectic and Enriques varieties.
Abstract: The purpose of this talk is to give an overview of the theory of primitive symplectic and primitive Enriques varieties, focusing mainly on the Enriques side. The former constitute singular and higher-dimensional analogues of K3 surfaces, while the latter can be viewed accordingly as singular and higher-dimensional analogues of Enriques surfaces. Specifically, I will present the basic properties as well as some examples of (smooth and singular) primitive Enriques varieties, making some comparisons with primitive symplectic varieties. I will also discuss a termination statement for so-called Enriques pairs and, if time permits, some deformation-theoretic results concerning primitive Enriques varieties. The talk will be based on joint works with F. Denisi, Á. D. Ríos Ortiz and Z. Xie.
September 16, 13:00
Speaker: Manuel Leal
Title: Birational geometry of quartic 3-folds.
Abstract: Let C be a smooth curve in projective 3-space, and let X be the blow-up of P3 along C. What is the birational geometry of X? How does it change when we specialize C? In this talk, we address these questions for a curve C of degree 10 and genus 11. In this case, the anticanonical model of X is a quartic 3-fold, which generically is linear determinantal. We analyze two different specializations of C, showcasing different behaviours, both in their birational geometry and as quartic 3-folds. Finally, we will discuss the relation of this problem with the Cremona group of birational automorphisms of P3. This is joint work with César Lozano Huerta and Montserrat Vite.
September 23, 14:00
Speaker: Georgios Politopoulos
Title: Computation of strata of differentials with spin parity.
Abstract: The purpose of this talk is to present computations of certain cycles on the moduli space of stable curves M_{g,n}(bar) arising from differentials and spin structures on curves. In the first part, I will provide a brief introduction to the moduli spaces of curves, tautological rings, and related moduli spaces. In the second part, we will focus on specific loci in M_{g,n}(bar), called strata of k-differentials, which parametrize stable curves admitting a k-differential with prescribed zeros and poles. A natural question is whether there is an explicit formula in the Chow ring of M_{g,n}(bar) for the Chow classes of these loci. When k and all the prescribed orders of zeros and poles are odd, we can define the so-called “spin refinement” of this problem. We will investigate an approach to these problems via (spin) double ramification cycles and demonstrate how they can be used to obtain formulas for the classes of strata of k-differentials and their spin refinements.
This talk is based on joint works Adrien Sauvaget and David Holmes.