Algebraic Geometry Seminar Spring 2013

The seminar meets on Fridays at 2:25 pm in Van Vleck B219.

The schedule for the previous semester is here.

Spring 2013

date	speaker	title	host(s)
January 25	Anatoly Libgober (UIC)	Albanese varieties of cyclic covers of plane, abelian varieties of CM type and orbifold pencils	Laurentiu
February 1	Laurentiu Maxim (University of Wisconsin-Madison)	Intersection spaces, perverse sheaves and type IIB string theory	local
March 1	Alexander Polishchuk (University of Oregon)	TBA	Dima
March 15	Xue Hang (Columbia)	On the height of a canonical point in the Jacobian of a genus four curve	Tonghai

Abstract

Anatoly Libgober

Albanese varieties of cyclic covers of plane, abelian varieties of CM type and orbifold pencils

I'll describe the relation between Alexander modules of plane algebraic curves and maps of their complements onto orbifolds. A key step is a description of the Albanese variety of cyclic covers of the plane in terms of abelian varieties of CM type.

Laurentiu Maxim

Intersection spaces, perverse sheaves and type IIB string theory

The method of intersection spaces associates rational Poincare complexes to singular stratified spaces. For a complex projective hypersurface with only isolated singularities, we show that the cohomology of the associated intersection space is the hypercohomology of a perverse sheaf, the intersection space complex, on the hypersurface. We will discuss properties of the intersection space complex, such as self-duality, its betti numbers and mixed Hodge structures on its hypercohomology groups. This is joint work with Banagl and Budur.