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

Forschungsseminar "Algebraische Geometrie"

Sommersemester 2015

Das Forschungsseminar findet mittwochs in der Zeit von 15:00 - 17:00 Uhr in der Rudower Chaussee 25, 12489 Berlin-Adlershof, Raum 2.006 (Haus 2, Erdgeschoss), statt.

Seminar: Algebraic Geometry an der FU

15.04.2015 Andreas Leopold Knutsen (University of Bergen)
Title: Moduli of nodal curves on K3 and abelian surfaces

Abstract: The study of nodal curves in the (complex) plane was initiated by Severi in the 20s. Results of Severi, Harris and Sernesi imply that the variety parametrizing plane nodal curves of any fixed degree and allowed geometric genus (so-called Severi varieties) is nonempty, smooth and irreducible of the expected dimension, and the family of curves has the expected number of moduli (meaning that their normalizations have the expected number of moduli). Similar questions are quite open on most other surfaces. In the talk I will present recent progress concerning the moduli problem on K3 and abelian surfaces, where the natural objects to consider are the varieties parametrizing nodal curves on the surfaces allowing the surfaces to move in suitable moduli spaces (so-called universal Severi varieties). It turns out that such families of curves have the expected number of moduli except possibly for finitely many cases (and two known exceptions in the case of smooth curves). The K3 case is work joint with Ciliberto, Flamini and Galati, and partially intersects recent results obtained by Kemeny. The abelian case is joint work with Lelli-Chiesa and Mongardi.
23.04.2015 (DONNERSTAG, RAUM 4.007) Rahul Pandharipande (ETH Zürich) und Dragos Oprea (University of California, San Diego)
Title Rahul Pandharipande: A compactification of the space of meromorphic differentials

Abstract: I will discuss a proposal for a compactification of the spaces of (C,w) where C is a nonsingular curve and w is a meromorphic differential with specified orders of zeros and poles. Joint work with G. Farkas.
Title Dragos Oprea: The Chern characters of the Verlinde bundles

Abstract: The Verlinde bundles are constructed over the moduli space of curves by considering relative moduli spaces of vector bundles. Their Chern characters yield a cohomological field theory. I will explain how Teleman's work on semisimple cohomological field theories can be used to derive explicit formulas for the Chern characters in terms of tautological classes. This is joint work with A. Marian, R. Pandharipande, A. Pixton and D. Zvonkine.
29.04.2015 Frank Gounelas (HU Berlin)
Title: To be announced

Abstract: To be announced.
06.05.2015 Alex Küronya (Budapest University of Technology and Economics)
Title: To be announced

Abstract: To be announced.
13.05.2015 Takehiko Yasuda (Osaka University, zzt. Max-Planck-Institut für Mathematik)
Title: To be announced

Abstract: To be announced.
20.05.2015 kein Seminar
27.05.2015 Alessandro Verra (Università Roma Tre)
Title: To be announced

Abstract: To be announced.
17.06.2015 Nicola Tarasca (University of Utah)
Title: To be announced

Abstract: To be announced.


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