Commutative Algebra Seminar

Title

Lyubeznik and Cech-de Rham numbers

Abstract

If Y is an affine variety inside CC^n cut out by the ideal I inside, and m a distinguished maximal ideal of, CC[x_1,…,x_n], one can attach two sets of numbers to them, either by applying the de Rham functor the D-module H^t_I(R), or the D-module restriction functor for the inclusion Spec(R/m)\into Spec R. It turns out that these numbers are in fact functions of Y and not of the embedding into an affine space.

In the talk we discuss known facts as well as some recent insights on these double arrays of numbers. This will include some general vanishing results, as well as a discussion on when the associated spectral sequence for which these arrays are the E_2-page, collapses.