Year: 2026
Type: preprint
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 $\mathbb{F}_q$-rational points and for the associated global $ζ$-functions.
Source: arXiv (Cornell University)
Author: Andrusov, Nikita
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221813489