The intersection cohomology Hodge module of toric varieties
Algebraic Geometry
2025-12-25 v4 Combinatorics
Abstract
We study the Hodge filtration of the intersection cohomology Hodge module for toric varieties. More precisely, we study the cohomology sheaves of the graded de Rham complex of the intersection cohomology Hodge module and give a precise formula relating it with the stalks of the intersection cohomology as a constructible complex. The main idea is to use the Ishida complex in order to compute the higher direct images of the sheaf of reflexive differentials.
Keywords
Cite
@article{arxiv.2404.04767,
title = {The intersection cohomology Hodge module of toric varieties},
author = {Hyunsuk Kim and Sridhar Venkatesh},
journal= {arXiv preprint arXiv:2404.04767},
year = {2025}
}
Comments
Current: 29 pages, added Appendix B and Remark 1.2. Previous: added Proposition 2.19 and minor changes