Commutative Algebra Seminar
Uli Walther
Purdue University
GKZ-systems and mixed Hodge modules
Abstract: I will define GKZ-systems, and talk a little about their properties from the
algebraic, analytic, and combinatorial point of view. Then I will
discuss a theorem of Gelfand et al, and a sharpening by Mathias Schulze and
myself, on the question which GKZ-systems arise as (D-module-)direct
image of a natural D-module on a torus. In such cases, the GKZ-system can
inherit a mixed Hodge module structure. I will then explain work with
Thomas Reichelt that computes the weight filtration of this MHM structure on a
class of GKZ-systems that comes up naturally in mirror symmetry. This
complements work of Reichelt and Christian Sevenheck who computed the Hodge
filtration, and supersedes computations of Batyrev who determined the
weight filtration in a generic point. Very few of such explicitly
computed structures seem to be known.
Monday November 19, 2018 at 11:00 AM in 427 SEO