PreprintCC BY 4.0HAL
The g-theorem in smooth approximation
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.
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BibTeX
@misc{hakavuori2026gtheorem,
title = {{The g-theorem in smooth approximation}},
author = {Joel Hakavuori},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24790},
eprint = {2609.24790},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05758926v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The g-theorem in smooth approximation
AU - Joel Hakavuori
PY - 2026
DA - 2026/09/21
PB - HAL
DO - 10.48550/arxiv.2609.24790
UR - https://hal.science/hal-05758926v1
AB - 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.
ER -