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

2020/06/06 by Kerr, Matt, Laza, Radu
#14D06 #14D07 #32S30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/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.

Related

• Hodge theory of degenerations, (III): a vanishing-cycle calculus for non-isolated singularities
• Hodge ideals and spectrum of isolated hypersurface singularities
• Hodge ideal and spectrum of weighted homogeneous isolated singularities
• The Spectrum of Hypersurface Singularities
• Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution