English

Triangulations of simplices with vanishing local h-polynomial

Combinatorics 2025-01-07 v2

Abstract

Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of triangulations of simplices whose local h-polynomial vanishes. As a first step, we identify a class of refinements that preserve the local h-polynomial. In dimensions 2 and 3, we show that all triangulations with vanishing local h-polynomial are obtained from one or two simple examples by a sequence of such refinements. In higher dimensions, we prove some partial results and give further examples.

Keywords

Cite

@article{arxiv.1909.10843,
  title  = {Triangulations of simplices with vanishing local h-polynomial},
  author = {André de Moura and Elijah Gunther and Sam Payne and Jason Schuchardt and Alan Stapledon},
  journal= {arXiv preprint arXiv:1909.10843},
  year   = {2025}
}

Comments

v2: 15 pages, 6 figures, minor expository improvements. To appear in Algebraic Combinatorics