*Humboldt-Universität zu Berlin *

*Mathem.-Naturwissenschaftliche Fakultät*

*Institut für Mathematik*

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 |
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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.
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15.05.2019 | 13:15 - 14:30 Mihai Paun (Universität Bayreuth) | |

Title: On the algebraicity of holomorphic foliations. |
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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.
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14:45 - 16:00 Rahul Pandharipande (ETH Zurich) | ||

Title: Virtual Euler characteristics of Quot scheme of surfaces. |
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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.
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22.05.2019 | Evgeny Shinder (University of Sheffield). | |

Title: Variation of stable birational types of hypersurfaces. |
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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..
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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. |
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Abstract: A discussion on some
problems for the upcoming
MATH+ Algebraic Geometry
Semester.
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05.06.2019 | Yohan Brunebarbe (CNRS Bordeaux). | |

Title: o-minimal geometry and algebraicity of period maps. |
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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..
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26.06.2019 | Seminar postponed until next week. | |

03.07.2019 | 13:15 - 14:30 Paweł Borówka (Uniwersytet Jagielloński Kraków). | |

Title: Klein coverings of genus 2 curves. |
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Abstract: In the talk, we will describe the geometry of etale 4:1
coverings of genus 2 curves given by a Klein group.
The moduli of such coverings has 2 connected components that aredistinguished by the value of the Weil pairing
on the group. We will show that in both cases, everything can be readfrom the 6 branch points of the curve.
As a main result, we will describe the Prym variety of a covering and
show that the Prym map is injective.
This is a joint work with Angela Ortega.
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14:45 - 16:00 Mario Kummer (Technische Universität Berlin). | ||

Title: Positive Definite Ulrich Bundles |
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Abstract: I will explain how Ulrich bundles and secant varieties of curves can be
used for approaching certain questions that arise in the theory of
convex optimization. This is joint work with Rainer Sinn.
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