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

Forschungsseminar "Algebraische Geometrie"

Sommersemester 2019

Das Forschungsseminar findet mittwochs in der Zeit von 13:00 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 1.114, statt.

Seminar: Algebraic Geometry an der FU

10.04.2019 Stefan Schreieder (LMU München)
Title: On deformations of quintic and septic hypersurfaces

Abstract: An old question of Mori asks whether in dimension at least three, any smooth specialization of a hypersurface of prime degree is again a hypersurface. A positive answer to this question has up till now only been known in degrees two and three. In this talk I explain how to settle the case of quintics (in arbitrary dimension) and septics in dimension three. Our results follow from numerical characterizations of the corresponding hypersurfaces. In the case of quintics, this extends famous work of Horikawa who analysed deformations of quintic surfaces. Joint work with J.C. Ottem.
15.05.2019 13:15 - 14:30 Mihai Paun (Universität Bayreuth)
Title: On the algebraicity of holomorphic foliations.

Abstract: We will report on a recent joint work with J. Cao and F. Campana. Our main result is an algebraicity criteria for holomorphic foliations with trivial first Chern class.
14:45 - 16:00 Rahul Pandharipande (ETH Zurich)
Title: Virtual Euler characteristics of Quot scheme of surfaces.

Abstract: Let S be a nonsingular projective surface. Quot schemes of quotients on S with supports of dimensions 0 and 1 always have 2-term obstruction theories (and therefore also have natural virtual fundamental classes). I will explain what we know about the virtual Euler characteristics in this theory: theorems, conjectures, and a lot of examples. Joint work with Dragos Oprea.
22.05.2019 Evgeny Shinder (University of Sheffield).
Title: Variation of stable birational types of hypersurfaces.

Abstract: I will explain the rationality problem for hypersurfaces of high degree, and show how the specialization for the Grothendieck ring of varieties allows to prove that very general hypersurfaces of high degree are not stably birational to each other..
04.06.2019 11 - 13 BMS Room Gavril Farkas (HU Berlin) and Bernd Sturmfels (MPI-MiS Leipzig and UC Berkeley).
Title: Problems for the MATH+ Algebraic Geometry program.

Abstract: A discussion on some problems for the upcoming MATH+ Algebraic Geometry Semester.
05.06.2019 Yohan Brunebarbe (CNRS Bordeaux).
Title: o-minimal geometry and algebraicity of period maps.

Abstract: In this talk I will introduce o-minimal geometry and illustrate its relevance to proving algebraicity of certain analytically defined objects. As an application, I will explain that the period maps associated to variations of pure Hodge structures are algebraic in corestriction to their image, as conjectured by Griffiths. This is joint work with Benjamin Bakker and Jacob Tsimerman..
26.06.2019 Stefan Kebekus (Universität Freiburg).
Title: Tba.

Abstract: Tba.
03.07.2019 Mario Kummer (Technische Universität Berlin).
Title: Tba.

Abstract: Tba.


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