Humboldt-Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik
Sommersemester 2024-2025
Time: Wednesday 13:15 - 14:45
Room: 3.007 John von Neumann-Haus
Humboldt Arithmetic Geometry Seminar
Seminar: Algebraic Geometry an der FU
| Time | Room | Speaker |
|---|---|---|
| 16.04.2025, 13:15h | Theodosis Alexandrou (HU Berlin) | |
| Title: Torsion higher Chow cycles modulo | ||
| Abstract: We study the injectivity property of exterior product maps of higher Chow groups on algebraic varieties. As an application for every \(p>1\) and for each \(d>p+3\) and \(n>1\), we establish the first examples of smooth complex projective \(d\)-folds \(X\) such that for all codimension \(c\) between \(p+ 3\) and \(d−1\), the higher Chow group of codimension \(c\) cycles on \(X\) contains infinitely many torsion cycles of order \(n\) that remain linearly independent modulo \(n.\) A crucial tool for the proof is morphic cohomology. | ||
| 7.05.2025, 13:15h | Robert Auffarth (Universidad de Chile) | |
| Title: Pseudoreflections on Prym varieties | ||
| Abstract: Smooth quotients of abelian varieties by finite groups were first studied by the author in an attempt to find Jacobian varieties of arbitrary dimension that split isogenously as the product of elliptic curves, the existence of which was brought into question by Ekedahl and Serre in the 1990s and remains an open question to this day. The author proved, along with G. Lucchini Arteche, that smooth quotients of Jacobian varieties by a finite group of geometric origin (i.e. that comes from an action on the curve) only exist up to dimension 3, thereby closing the door on this approach to the Ekedahl-Serre question. Leaving this question behind, it is natural to ask if one can characterize smooth quotients of Prym varieties by finite groups. In this talk we will describe the moduli space of Prym varieties that possess a pseudoreflection, and therefore a smooth quotient, of geometric origin (i.e. the action comes from a certain action on curves). In particular, we will prove that examples exist in arbitrary dimensions. This is joint work with Martí Lahoz and Juan Carlos Naranjo. | ||
| 14.05.2025, 13:15 - 14:15 | Jenia Tevelev (University of Massachusetts Amherst) | |
| Title: Semi-orthogonal decompositions of Fano varieties and moduli spaces | ||
| Abstract: The study of fully faithful functors, including equivalences, between derived categories of smooth projective varieties (or, more generally, smooth proper triangulated categories) is, in many ways, analogous to the study of rational contractions in the minimal model program. For a Fano manifold, homological mirror symmetry predicts that its derived category admits canonical semi-orthogonal decompositions (related by the braid group action) with remarkable properties, such as compatibility with rational contractions. After discussing this motivation, I will survey potential constructions of canonical semi-orthogonal decompositions, focusing on the case where the Fano manifold is a moduli space of stable objects of some type on another manifold and where its birational geometry can be understood as a variation of the stability condition. As an application, we will construct the canonical semi-orthogonal decomposition of the derived category of the moduli space of stable vector bundles of rank 2 with a fixed determinant of odd degree on a smooth projective curve. When the degree is even, the moduli space is singular, and the construction provides canonical semi-orthogonal decompositions of its quasi-BPS categories; for example, they are compatible with the Hecke correspondence. | ||
| 14.05.2025, 14:30 - 15:30 | Marian Aprodu (University of Bucharest) | |
| Title: Resonance of vector bundles | ||
| Abstract: I will report on a joint work in progress with C. Spiridon. Resonance varieties are projective varieties covered by lines, defined as images - via incidence varieties - of linear sections of Grassmannians of lines in a given projective space. These varieties originate in the study of hyperplane arrangement groups, and today they play a significant role in geometric group theory. Building on previous joint works with G. Farkas, C. Raicu, A. Suciu, and J. Weyman, we continue the investigation of resonance varieties associated with vector bundles, with particular emphasis on the case where the linear section is transversal. For the Grassmannian \(G(2,6)\), our work is directly connected to Mukai's canonical model of general curves of genus 8. | ||
| 25.06.2025, 13:15h | Shigeru Mukai (Kyoto) | |
| Title: TBA | ||
| Abstract: | ||