Mixed Hodge structure in the cohomology of moment-angle complexes
Abstract
This work studies the relationship between the multigrading in the cohomology of moment-angle complexes, introduced by V. Buchstaber and T. Panov in their computation of these cohomology groups, and the multigrading in the cohomology of the corresponding complements of coordinate subspace arrangements, arising from the mixed Hodge structure. It is shown that these multigradings coincide. This result refines a theorem from Yu. Eliyashev's 2013 dissertation. Furthermore, results on the mixed Hodge structure in the cohomology of complements of coordinate subspace arrangements are applied to the study of the same varieties over finite fields. In particular, various formulas are obtained for the number of 𝔽q-rational points and for the associated global ζ-functions.
Related
- Products in absolute Hodge cohomology and mixed Hodge formality
- Generic vanishing for Dolbeault cohomology of mixed Hodge modules on abelian varieties
- Du Bois cohomology of noncommutative spaces and the Hodge numbers invariance conjecture for singular varieties
- A Hodge module construction of relative Du Bois complexes
- Hodge--Deligne polynomials and Sn-representations on the cohomology of ℳ̅2,n
BibTeX
@misc{andrusov2026mixed,
title = {{Mixed Hodge structure in the cohomology of moment-angle complexes}},
author = {Nikita Andrusov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16230},
eprint = {2610.16230},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16230},
}
RIS
TY - UNPB
TI - Mixed Hodge structure in the cohomology of moment-angle complexes
AU - Nikita Andrusov
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16230
UR - https://arxiv.org/abs/2610.16230
AB - This work studies the relationship between the multigrading in the cohomology of moment-angle complexes, introduced by V. Buchstaber and T. Panov in their computation of these cohomology groups, and the multigrading in the cohomology of the corresponding complements of coordinate subspace arrangements, arising from the mixed Hodge structure. It is shown that these multigradings coincide. This result refines a theorem from Yu. Eliyashev's 2013 dissertation. Furthermore, results on the mixed Hodge structure in the cohomology of complements of coordinate subspace arrangements are applied to the study of the same varieties over finite fields. In particular, various formulas are obtained for the number of 𝔽_q-rational points and for the associated global ζ-functions.
ER -