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

Forschungsseminar "Arithmetische Geometrie"

Wintersemester 2018/19


Das Forschungsseminar findet dienstags in der Zeit von 13:15 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 3.006 (Haus 3, Erdgeschoss), statt.


23.10.2018 Giulio Codogni (Uni Roma Tre)
Title: Gauss map, singularities of the theta divisor and trisecants
Abstract: The Gauss map is a finite rational dominant map naturally defined on the theta divisor of an irreducible principally polarised abelian varieties. In the first part of this talk, we study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. Thanks to this analysis, we obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus. We spell out this bound in several examples, and we use it to understand the local structure of isolated singular points. We further define a stratification of the moduli space of ppavs by the degree of the Gauss map. In dimension four, we show that this stratification gives a weak solution of the Schottky problem, and we conjecture that this is true in any dimension. This is a joint work with S. Grushevsky and E. Sernesi. In the second part of this talk, we will study the relation between the Gauss map and trisecant of the Kummer variety. Fay's trisecant formula shows that the Kummer variety of the Jacobian of a smooth projective curve has a four dimensional family of trisecant lines. We study when these lines intersect the theta divisor of the Jacobian, and prove that the Gauss map of the theta divisor is constant on these points of intersection, when defined. We investigate the relation between the Gauss map and multisecant planes of the Kummer variety as well. This is a joint work with R. Auffarth and R. Salvati Manni.
30.10.2018 Nero Budur (KU Leuven)
Title: Tba
Abstract: Tba.
06.11.2018 Peter Jossen (ETH Zürich)
Title: Tba
Abstract: Tba.
13.11.2018 Speaker: Tba
Title: Tba
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20.11.2018 Speaker: Tba
Title: Tba
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27.11.2018 Speaker: Tba
Title: Tba
Abstract: Tba.
04.12.2018 Speaker: Tba
Title: Tba
Abstract: Tba.
11.12.2018 Speaker: Tba
Title: Tba
Abstract: Tba.
18.12.2018 Christian Liedtke (TU München)
Title: Tba
Abstract: Tba.


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