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

Forschungsseminar "Algebraische Geometrie"

Sommersemester 2017

Das Forschungsseminar findet mittwochs in der Zeit von 13:00 - 15:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 2.006, statt.

Seminar: Algebraic Geometry an der FU

19.04.2017 Alessandro Verra (U Roma 3)
Title: On quasi étale coverings of K3 surfaces and their moduli

Abstract: Let X be a complex K3 surface endowed with a cyclic group G of order n of symplectic automorphisms. Then Y := X/G is a normal K3 surface and the quotient map from X to Y is a quasi étale cover. The talk will survey about the well known classification of the families of these surfaces Y and on some recent advances in the study of their geometric properties and of their moduli. The case n = 3, of triple covers, will be specially considered, together with some applications to the study of the moduli spaces of étale triple covers of curves of genus g, g < 6.
26.04.2017 Rahul Pandharipande (ETH Zürich)
Title: Cohomological field theories from local curves

Abstract: I will explain work in progress with H.H. Tseng on the higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and its relationship to local curve theories.
03.05.2017 kein Seminar
10.05.2017 kein Seminar
17.05.2017 Juan Carlos Naranjo (U Barcelona)
Title: On the Xiao conjecture for fibred surfaces

Abstract: Xiao's conjecture deals with the relation between the natural invariants present on a fibred surface ƒ : SB: the irregularity q of S, the genus b of the base curve B and of the genus g of the fibre of ƒ. In a paper with M. A. Barja and V. González-Alonso we have proved the inequality qbgc, where c is the Clifford index of the generic fibre. This gives in particular a proof of the (modified) Xiao's conjecture, qbg / 2+1, for fibrations whose general fibres have maximal Clifford index. In this talk we will report on that paper and also on a recent progress on the Xiao's conjecture for fibrations whose generic fibre is a plane curve. More precisely in a joint work with F. Favale an G. P. Pirola we have proved the conjecture for fibrations of quintic plane curves, we also have proved the inequality qbgc − 1 for fibrations of plane curves of any degree ≥ 5.
24.05.2017 Marco Ramponi (U Poitiers)
Title: Curves on K3 double covers of Enriques surfaces

Abstract: Recent works by Farkas and Kemeny on the Green-Lazarsfeld and Prym-Green conjectures rely on the possibility of computing Clifford indices and gonalities of curves on special K3 surfaces. In this talk we consider curves lying on K3 surfaces X carrying a fixed-point free involution. Such an automorphism is also called an Enriques involution, since the quotient of X by it is an Enriques surface. Building on work by Knutsen and Lopez around the Brill-Noether theory for curves on Enriques surfaces, we show that the gonality and the Clifford index of all curves on X is governed by the genus 1 fibrations carried by the K3 surface X and coming from the Enriques quotient.
31.05.2017 Patrick Graf (U Bayreuth)
Title: Finite quotients of complex tori

Abstract: Let X be a compact Kähler threefold with canonical singularities and vanishing first Chern class. I will show that if the second orbifold Chern class of X intersects some Kähler form trivially, then X admits a quasi-étale (i.e. étale in codimension one) cover by a complex torus. This result generalizes a theorem of Shepherd-Barron and Wilson for projective varieties. It should be seen as complementing the structure theory of Kähler threefolds (aka Minimal Model Program).
Part of the talk is devoted to explaining the notion of second orbifold Chern class for complex spaces with canonical singularities, since this topic has not been treated in the literature up to now. If time permits, I will also discuss possible generalizations to klt singularities and to higher dimensions. Joint with Tim Kirschner (Essen).
07.06.2017 András Némethi (Rényi Institute Budapest)
Title: t.b.a.

Abstract: t.b.a.
14.06.2017 t.b.a.
21.06.2017 Peter Bürgisser (TU Berlin)
Title: t.b.a.

Abstract: t.b.a.
05.07.2017 Samuel Grushevsky (Stony Brook University)
Title: t.b.a.

Abstract: t.b.a.
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