paper

Hodge theory of degenerations, (II): vanishing cohomology and geometric applications

arXiv:2006.03953

Abstract

We study the weighted spectrum and vanishing cohomology for several classes of isolated hypersurface singularities, and how they contribute to the limiting mixed Hodge structure of a smoothing. Applications are given to several types of singularities arising in KSBA and GIT compactifications and mirror symmetry, including nodes on odd-dimensional hypersurfaces, $k$ -log-canonical and $k$ -rational singularities, and singularities with Calabi-Yau tail.

43 pages, version to appear in "Current Developments in Hodge Theory" (Proceedings of Hodge Theory at IMSA)