Limits of Hodge structures via D-modules


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November 16, 2021 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Qianyu Chen - Stony Brook University

It is well-known that each cohomology group of a compact K\"ahler manifold carries a Hodge structure. If we consider a degeneration of compact K\”ahler manifolds over a disk then it is natural to ask how the Hodge structures of smooth fibers degenerate. When the degeneration only allows a reduced singular fiber with simple normal crossings (i.e. semistable), Steenbrink constructed the limit of Hodge structure algebraically. A consequence of the existence of the limit of Hodge structure is the local invariant cycle theorem: the cohomology classes invariant under monodromy action come from the cohomology classes of the total space. In this talk, I will try to explain a method using D-modules to construct the limit of Hodge structure even when the degeneration is not semistable.