Year: 2026
Type: preprint
Abstract: We show that a sequence of simplicial polytopes approximating a smooth convex body has primitive Betti numbers diverging from the upper bound given by the $g$-theorem. This complements a result of Adiprasito-Nevo-Samper, who proved the corresponding divergence from the lower bound. The proof uses a new lower bound for the size of the shadow of a set of monomials.
Source: arXiv (Cornell University)
Author: Hakavuori, Joel
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214001944