Difference between revisions of "Algebraic Geometry Seminar Spring 2013"

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(Spring 2013)
(Anatoly Libgober)
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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.
 
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.
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===Laurentiu Maximr===
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''Intersection spaces, perverse sheaves and type IIB string theory''
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The method of intersection spaces associates rational Poincare complexes to singular stratified spaces. For a complex projective hypersurface with only isolated singularities,
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we show that the cohomology of the associated intersection space is the hypercohomology of a perverse sheaf, the intersection space complex, on the hypersurface.
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We will discuss properties of the intersection space complex, such as self-duality, its betti numbers and mixed Hodge structures on its hypercohomology groups.
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This is joint work with Banagl and Budur.

Revision as of 18:39, 22 January 2013

The seminar meets on Fridays at 2:25 pm in Van Vleck B215.

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) TBA 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 Maximr

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.