Algebraic Geometry Seminar Spring 2013
The seminar meets on Fridays at 2:25 pm in Van Vleck B215.
The schedule for the previous semester is here.
|January 25||[www.math.uic.edu/~libgober/ 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)||TBA||Tonghai|
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.
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.