Humboldt Universität zu Berlin
Mathem.Naturwissenschaftliche Fakultät II
Institut für Mathematik
Sommersemester 2014
Das Forschungsseminar findet mittwochs in der Zeit von 15:00  17:00 Uhr in der Rudower Chaussee 25, 12489 BerlinAdlershof, Raum 2.009 (Haus 2, Erdgeschoss), statt.
Seminar: Algebraic Geometry an der FU
16.04.2014  Alessandro Verra (Università Roma Tre) 
Title: Sixdimensional Pryms and FanoEnriques threefolds  
Abstract: The talk surveys some natural relations between the moduli spaces of Prym varieties and that of Enriques surfaces in genus at most 6. Then new relations are presented between R_{7} and the family of FanoEnriques threefolds which are linear sections of the variety of rank two quadrics in the threedimensional projective space. This leads to a geometric description of the universal singular locus of the Prym theta divisor over R_{7} and to a proof of its rational connectedness. 

23.04.2014  Gavril Farkas (HU Berlin) 
Title: What is the general principally polarized abelian variety of dimension six?  
Abstract: The general principally polarized abelian variety of dimension at most five is known to be a Prym variety. This reduces the study of abelian varieties of small dimension to the beautifully concrete theory of algebraic curves. I will discuss recent progress on finding a structure theorem for principally polarized abelian varieties of dimension six, and the implications this uniformization result has on the geometry of the moduli space A_{6}. 

30.04.2014  kein Seminar 
07.05.2014  kein Seminar 
14.05.2014  Michael Kemeny (HU Berlin) 
Title: Singular Curves on K3 Surfaces  
Abstract: In this talk we discuss the moduli space of smooth curves with a nodal model on a K3 surface. We will show that this space has the maximal possible dimension in most cases, as well as attempts to describe it via BrillNoether theory and Gaussiantype conditions.  
21.05.2014  Alina Marian (Northeastern University) 
Title: Geometry of the Verlinde sheaves  
Abstract: The Verlinde sheaves on the moduli space of curves arise by considering relative moduli spaces of vector bundles over M_{g}. They can also be constructed on the moduli spaces of K3 and abelian surfaces. I will review the construction and will describe recent progress understanding the geometry in all three settings  curves, abelian and K3 surfaces  with an emphasis on the case of curves.  
28.05.2014  Juan Carlos Naranjo (Universitat de Barcelona) 
Title: Isogenies of Jacobians  
Abstract: We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical BabbageEnriquesPetri theorem that the Jacobian variety of a generic element of a k codimensional subvariety of M_{g} is not isogenous to a distinct Jacobian if g>3k+4. We extend this result to k=1, g\ge 5 by using degeneration methods. This is a joint work with G.P. Pirola and V. Marcucci. 

16:30 Uhr  Charles Siegel (Kavli IPMU, Japan) 
Title: Trees and an Affine Cover of M_{0,n+1}  
Abstract: I will talk about work in progress, with Satoshi Kondo (Kavli IPMU) and Jesse Wolfson (Northwestern), on a covering of of the moduli of genus 0 marked curves by open affine subvarieties determined by rooted trees and constructed via Kapranov's model in terms of the blow up of projective space along linear subvarieties.  
04.06.2014  Yohan Brunebarbe (MPI Bonn) 
Title: Symmetric differentials and variations of Hodge structures  
Abstract: Let U be a smooth algebraic complex variety and X be a compactification such that the complementary D = X  U has simple normal crossings. In my talk I will explain how the existence on U of a nontrivial Zpolarized variation of Hodge structures forces the existence of nonzero logarithmic symmetric differential forms on the pair (X,D), i.e. sections of symmetric powers of the logarithmic cotangent bundle of the pair (X,D). This extends to the noncompact case one of the main result of a previous joint work with B. Klingler and B. Totaro. I will also discuss some applications to smooth quotients of bounded symmetric domains by arithmetic groups and to moduli spaces of curves and polarized K3 surfaces. 

11.06.2014  kein Seminar 
18.06.2014  Sebastian CasalainaMartin (University of Colorado, Boulder) 
Title: Prym varieties and applications  
Abstract: Prym varieties are abelian varieties obtained from connected, etale double covers of curves. They were introduced by Mumford (1974) in connection with the study the intermediate Jacobian of a cubic threefold, and were later used by Beauville (1977) to extended Mumford's construction to the case of arbitrary fibrations in odd dimensional quadrics. In this talk, I will review these constructions and then discuss a few recent projects building on this work. This will include degenerations of intermediate Jacobians, extensions of the Prym map, and the cohomology of fibrations in quadrics over the rational numbers. This is joint work with (in various combinations) S. Grushevsky, K. Hulek, R. Laza and J. Achter.  
25.06.2014  Jesse Kass (University of Michigan) 
Title: What is the limit of a line bundle on a nonnormal variety?  
Abstract: On a nonnormal variety, the limit of a family of line bundles is not always a line bundle. What is the limit? I will present an answer to this question and give some applications. If time permits, I will discuss connections with autoduality for the compactified Jacobian and with recent divisor class group computations of R. Hartshorne and C. Polini.  
02.07.2014  kein Seminar 
09.07.2014  Balázs Szendrői (University of Oxford) 
Title: Euler characteristics of Hilbert schemes of points of ADE surfaces  
Abstract: Given a smooth surface, the generating series of Euler characteristics of its Hilbert schemes of points can be given in closed form by (a specialisation of) Goettsche's formula. I will discuss a generalisation of this formula to surfaces with rational double points, built from the representation theory of affine Lie algebras. (Joint work with Adam Gyenge, Budapest)  
16.07.2014  kein Seminar 