Hodge theory of degenerations, (III): a vanishing-cycle calculus for non-isolated singularities
Matt Kerr and Radu Laza
Journal of Singularities
volume 29 (2026), 175-198
Received: 22 January 2024. In revised form: 7 September 2026
Abstract:
We continue our study of the Hodge theory of degenerations, initiated in Part I - general theory and Part II - geometric applications in the isolated singularity case. The focus here is on concrete computations in the case of non-isolated singularities, particularly those for which the singular locus has dimension one. These examples are significantly more involved than in the previous parts, and include k-log-canonical singularities, several specific surface singularities (both slc and non-slc), and certain singular 5-folds arising in the study of Feynman integrals.
Author(s) information:
Matt Kerr
Washington University in St. Louis
Department of Mathematics and Statistics
St. Louis, MO 63130-4899
email: matkerr@math.wustl.edu
Radu Laza
Stony Brook University
Department of Mathematics
Stony Brook, NY 11794-3651
email: rlaza@math.stonybrook.edu