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.
|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|
|April 19||Xavier Gomez-Mont (CIMAT, Guanajuato, Mexico)||TBA||Laurentiu|
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.
On the height of a canonical point in the Jacobian of a genus four curve
In this talk, we construct a quadratic point in the Jacobian of a non-hyperelliptic curve of genus four over a global field. We then compute the Neron--Tate height of this point in terms of the self-intersection of the admissible dualizing sheaf and some canonically defined local invariants. We show that the height of this point satisfies the Northcott property. We also give some estimates of the local invariants that appear in the height computation. When the reduction of the curve is simple, we compute explicitly the local invariants.