Sergey Yuzvinsky : RESONANCE VARIETIES OF HYPERPLANE COMPLEMENTS

Posted by , part of the Departmental Colloquium.

At

April 9, 2010, 3 p.m.

In

SEO 636

Abstract

The idea to view the cohomology ring A^* of a space as a cochain complex with the differential d_a (a \in A^1 ) given by the multiplication by a appeared first in the Farber-Novikov spectral sequence. The first sheet of the sequence is formed by cohomology H^* (A^* , d_a ). For a compact space X the sequence converges to the cohomology of X with local coefficients determined by a. Independently the cochain complex has been studied for complex hyperplane arrangement compelments which led to the notion of resonance varieties. These varieties will constitute the main character of the talk. Recently they have been related to classical geometric structures on the complex projective plane, pencils of algebraic curves, and also the Bernstein-Sato polynomials. If time allows, we will briefly discuss some generalizations of properties of the resonance varieties to other classes of spaces.