The $F$-pure threshold of a determinantal ideal

TL;DR

This paper computes the $F$-pure thresholds, a measure of singularity severity in prime characteristic, for determinantal ideals generated by minors of a generic matrix, bridging characteristic p and zero singularity invariants.

Contribution

The paper provides explicit calculations of the $F$-pure thresholds for determinantal ideals, a class of ideals important in algebraic geometry and commutative algebra.

Findings

Explicit formulas for $F$-pure thresholds of determinantal ideals

Connection established between $F$-pure thresholds and classical singularity invariants

Advancement in understanding singularities in prime characteristic

Abstract

The $F$-pure threshold is a numerical invariant of prime characteristic singularities, that constitutes an analogue of the log canonical thresholds in characteristic zero. We compute the $F$-pure thresholds of determinantal ideals, i.e., of ideals generated by the minors of a generic matrix.