The theory of F-rational signature
Abstract
F-signature is an important numeric invariant of singularities in positive characteristic that can be used to detect strong F-regularity. One would like to have a variant that rather detects F-rationality, and there are two theories that aim to fill this gap: F-rational signature of Hochster and Yao and dual F-signature of Sannai. Unfortunately, several important properties of the original F-signature are unknown for these invariants. We give a modification of the Hochster-Yao definition that agrees with Sannai's dual F-signature and push further the united theory to achieve a complete generalization of F-signature.
Cite
@article{arxiv.1911.02642,
title = {The theory of F-rational signature},
author = {Ilya Smirnov and Kevin Tucker},
journal= {arXiv preprint arXiv:1911.02642},
year = {2023}
}
Comments
Minor revision: Proposition 3.5 is now stated for arbitrary ideals and section 2.2.1 was added to show semicontinuity on the Grassmannian. Comments are still welcome