# ALGEBRAIC COMBINATORICS

Triangulations of simplices with vanishing local $h$-polynomial
Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1417-1430.

Motivated by connections to intersection homology of toric morphisms, the motivic monodromy conjecture, and a question of Stanley, we study the structure of geometric 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 geometric 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.

Revised: 2020-08-19
Accepted: 2020-08-20
Published online: 2020-12-04
DOI: https://doi.org/10.5802/alco.146
Classification: 05E45
Keywords: local $h$-polynomials, triangulations of simplices, geometric triangulations
@article{ALCO_2020__3_6_1417_0,
author = {de Moura, Andr\'e and Gunther, Elijah and Payne, Sam and Schuchardt, Jason and Stapledon, Alan},
title = {Triangulations of simplices with vanishing local <span class="mathjax-formula">$h$</span>-polynomial},
journal = {Algebraic Combinatorics},
pages = {1417--1430},
publisher = {MathOA foundation},
volume = {3},
number = {6},
year = {2020},
doi = {10.5802/alco.146},
language = {en},
url = {alco.centre-mersenne.org/item/ALCO_2020__3_6_1417_0/}
}
de Moura, André; Gunther, Elijah; Payne, Sam; Schuchardt, Jason; Stapledon, Alan. Triangulations of simplices with vanishing local $h$-polynomial. Algebraic Combinatorics, Volume 3 (2020) no. 6, pp. 1417-1430. doi : 10.5802/alco.146. https://alco.centre-mersenne.org/item/ALCO_2020__3_6_1417_0/

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