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A complete classification of negative stringy Hodge numbers
Abstract
The stringy E-function is a fundamental invariant of varieties with log-terminal singularities, which was introduced by Batyrev as a singular analogue of the Hodge--Deligne polynomial. Its coefficients (up to an appropriate sign) are the stringy Hodge numbers hstrp,q(Y). We completely determine when these coefficients are universally non-negative:~for each triple (n,p,q), we classify when hstrp,q(Y)≥ 0 for every projective Gorenstein canonical n-fold Y; we answer this question both when we assume Estr(Y;u,v) is a polynomial and when we drop this condition. As a consequence, we settle Batyrev's non-negativity conjecture in all dimensions:~it holds in dimensions at most $4$ and fails in every dimension at least $5$.
Related
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BibTeX
@misc{huang2026complete,
title = {{A complete classification of negative stringy Hodge numbers}},
author = {Jiahui Huang and Matthew Satriano},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.07836},
eprint = {2608.07836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07836},
}
RIS
TY - UNPB
TI - A complete classification of negative stringy Hodge numbers
AU - Jiahui Huang
AU - Matthew Satriano
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2608.07836
UR - https://arxiv.org/abs/2608.07836
AB - The stringy E-function is a fundamental invariant of varieties with log-terminal singularities, which was introduced by Batyrev as a singular analogue of the Hodge--Deligne polynomial. Its coefficients (up to an appropriate sign) are the stringy Hodge numbers h_str^p,q(Y). We completely determine when these coefficients are universally non-negative:~for each triple (n,p,q), we classify when h_str^p,q(Y)≥ 0 for every projective Gorenstein canonical n-fold Y; we answer this question both when we assume E_str(Y;u,v) is a polynomial and when we drop this condition. As a consequence, we settle Batyrev's non-negativity conjecture in all dimensions:~it holds in dimensions at most $4$ and fails in every dimension at least $5$.
ER -