Waldschmidt constants for Stanley–Reisner ideals of a class of simplicial complexes

Abstract

Abstract. We study the symbolic powers of the Stanley-Reisner ideal IB n of a bipyramid Bn over a n−gon Qn. Using a combinatorial approach, based on analysis of subtrees in Qn we compute the Waldschmidt constant of IB n .

Initial sequences and Waldschmidt constants of planar point configurations

“…They are also quite interesting invariants studied in their own right, see e.g. [1], [2], [7], [15].…”

Lower semi-continuity of the Waldschmidt constants

“…Therefore I [2] = J [3] where J = Γ * (J ) in R. Note that J = (x, y 2 ) from direct calculation, and since −E 1 − E 2 satisfies the proximity inequalities,…”

Waldschmidt Constants for Stanley–Reisner Ideals of a Class of Graphs

“…For n = 4 the bipyramid B 4 is indicated in Figure 1. We have The main result of [2] is the following Theorem ([2, Theorem 1.1]). This Theorem has been already reproved in [1, Theorem 6.10], the authors appeal however to fractional chromatic numbers of hypergraphs and use the advanced machinery developed in their paper.…”

“…By the way of an example we mention here only the following one. Our research here has been motivated by [2], where Bocci and Franci initiated the study of Waldschmidt constants of monomial ideals determined by some combinatorial data. They have computed Waldschmidt constants of Stanley-Reisner ideals of bipyramids (see Section 2.2).…”