Waldschmidt constants for Stanley-Reisner ideals of a class of Simplicial Complexes

TL;DR

This paper computes the Waldschmidt constants for Stanley-Reisner ideals of bipyramids over polygons using combinatorial methods, advancing understanding of symbolic powers in algebraic combinatorics.

Contribution

It introduces a combinatorial approach to determine Waldschmidt constants for a specific class of Stanley-Reisner ideals associated with bipyramids.

Findings

Waldschmidt constants are explicitly computed for bipyramid ideals.

The approach links combinatorial structures to algebraic invariants.

Results enhance understanding of symbolic powers in combinatorial commutative algebra.

Abstract

We study the symbolic powers of the Stanley-Reisner ideal $I_{B_n}$ of a bipyramid $B_n$ over a $n-$gon $Q_n$. Using a combinatorial approach, based on analysis of subtrees in $Q_n$ we compute the Waldschmidt constant of $I_{B_n}$.