На главную страницу НМУ

Susumu Tanabe

The Hodge structure of the cohomology of algebraic varieties

First of all I would like to mention about the vanishing cohomology associated to the Milnor fibre of the isolated hypersurface singularity. We review the results on the Milnor number (local and global) by Kouchnirenko (Inventiones math. 32, No1 (1976), 1-32) and then roughly sketch the formula of Hodge numbers given by Danilov (FAA, 13, No.2(1979),32-47). I will draw pictures of polyhedron and integer points for several examples.

The Hodge structure of the cohomology of an affine hypersurface in an algebraic torus will be discussed. The notion of Erhart polynomial will be introduced and used to calculate the Hodge numbers. Both Hodge and weight filtrations allow purely combinatorial discription of integer points located on a polyhedron. The fundamental literature on this subject is several articles by V.Batyrev (e.g. Duke v.69, No.2, 1993).

Rambler's Top100