Humboldt-Universität zu Berlin
Mathem.-Naturwissenschaftliche Fakultät
Institut für Mathematik

Forschungsseminar "Algebraische Geometrie"

Sommersemester 2024


Time: Wednesday 13:15 - 14:45

Room: 3.007 John von Neumann-Haus

Humboldt Arithmetic Geometry Seminar

Seminar: Algebraic Geometry an der FU


TimeRoomSpeaker
THURSDAY 18.04.2024, 13:15h Gregory Pearlstein (Pisa)
Title: KSBA stable limits associated to quasi-homogeneous surface singularities
Abstract: Smooth minimal surfaces of general type with \(K^2=1\), \(p_g=2\), and \(q=0\) constitute a fundamental example in the geography of algebraic surfaces. The moduli space of their canonical models admits a modular compactification \(M\) via the minimal model program. In previous work with Patricio Gallardo and Luca Schaffler we constructed eight new irreducible boundary divisors in \(M\) arising from unimodal singularities. In this talk, we will discuss extension of this work to quasi-homogeneous surface singularities.
15.05.2024, 13:15h Nazim Khelifa (IHES)
Title: Density criteria for typical Hodge loci and applications
Abstract: After recalling the Zilber-Pink paradigm introduced in Hodge theory by Klingler and further developed by Baldi-Klingler-Ullmo, I will present joint work with David Urbanik giving sufficient conditions that ensure that the Hodge locus, i.e. the locus in the base of an integral polarized variation of Hodge structures where the fibers acquire non-generic Hodge tensors, is dense for the complex analytic topology in the base. I will then explain how to relate this result to classical results on Noether-Lefschetz loci. Finally, I will explain how the current knowledge of the Hodge locus can be used to revisit and improve classical bounds on the dimension of the image of period maps, studied among others by Carlson, Griffiths, Kasparian, Mayer and Toledo.
22.05.2024, 13:00-14:00h Alexandru Suciu (Northeastern University)
Title: The Milnor fibrations of hyperplane arrangements
Abstract: To each multi-arrangement \((A,m)\), there is an associated Milnor fibration of the complement \(M=M(A)\). Although the Betti numbers of the Milnor fiber \(F=F(A,m)\) can be expressed in terms of the jump loci for rank 1 local systems on \(M\), explicit formulas are still lacking in full generality, even for \(b_1(F)\). After introducing these notions and explaining some of the known results, I will consider the "generic" case, in which \(b_1(F)\) is as small as possible. I will describe ways to extract information on the cohomology jump loci, the lower central series quotients, and the Chen ranks of the fundamental group of the Milnor fiber in this situation.
22.05.2024, 14:15-15:15h Marian Aprodu (University of Bucharest)
Title: Resonance, syzygies, and rank-3 Ulrich bundles on the del Pezzo threefold \(V_5\)
Abstract: This is a joint work with Yeongrak Kim. We investigate a geometric criterion for a smooth curve of genus 14 and degree 18 to be described as the zero locus of a section in an Ulrich bundle of rank 3 on a del Pezzo threefold \(V_5\). The main challenge is to read off the Pfaffian quadrics defining \(V_5\) from geometric properties of the curve. We find that this problem is related to the existence of a special rank-two vector bundle on the curve, with trivial resonance. From an explicit calculation of the Betti table, we also deduce the uniqueness of the del Pezzo threefold.
30.05.2024-31.05.2024 Workshop Curves, abelian varieties, and their moduli at HU Berlin
Curves, abelian varieties, and their moduli
TUESDAY 04.06.2024, 13:15h ROOM 3.006 Richard Rimanyi (University of North Carolina)
Title:
Abstract:
19.06.2024, 13:15h Carl Lian (Tufts University)
Title:
Abstract:
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