Extending resurgence bounds from matroid configurations of points to Stanley–Reisner ideals

Ascertain whether the known upper bounds for resurgence and asymptotic resurgence that hold for matroid configurations of points also hold for the resurgence and asymptotic resurgence of the Stanley–Reisner ideal I_{Δ(M)} itself (without specialization).

Background

For matroid configurations of points (specializations with N = n−k), the paper recalls and applies general bounds on resurgence and asymptotic resurgence in terms of regularity, generators, and Waldschmidt constants. These rely on zero-dimensionality or smoothness.

Whether analogous upper bounds extend to the nonspecialized Stanley–Reisner ideals of matroids, which need not define zero-dimensional or smooth schemes, is posed as an open question.