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Hodge Theory and Grobner Degenerations
Abstract
In this paper, we investigate the behavior of mixed Hodge structures under square-free Grobner degenerations. We show that the weight-zero part of singular cohomology and the zeroth graded piece of the Hodge filtration are preserved under such degenerations, complementing the homological rigidity established in the seminal work of Conca and Varbaro. We use these results to settle their conjecture concerning the singularities of homogeneous coordinate rings admitting such degenerations.
Related
- Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture
- Singular Hodge theory for combinatorial geometries
- Hodge theory on metric spaces
- p-adic Hodge theory of unipotent completions revisited
- Hodge theory and topology of Bogomolov--Guan manifolds
BibTeX
@misc{ramkumar2026hodge,
title = {{Hodge Theory and Grobner Degenerations}},
author = {Ritvik Ramkumar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34641},
eprint = {2610.34641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34641},
}
RIS
TY - UNPB
TI - Hodge Theory and Grobner Degenerations
AU - Ritvik Ramkumar
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34641
UR - https://arxiv.org/abs/2610.34641
AB - In this paper, we investigate the behavior of mixed Hodge structures under square-free Grobner degenerations. We show that the weight-zero part of singular cohomology and the zeroth graded piece of the Hodge filtration are preserved under such degenerations, complementing the homological rigidity established in the seminal work of Conca and Varbaro. We use these results to settle their conjecture concerning the singularities of homogeneous coordinate rings admitting such degenerations.
ER -