Extensions of two Chow stability criteria to positive characteristics

TL;DR

This paper extends two criteria for Chow stability to positive characteristic fields, analyzing hypersurfaces and log canonical thresholds, and discusses properties of log-canonicity with examples, including stability of cycle sums.

Contribution

It introduces new extensions of Chow stability criteria to positive characteristics and explores properties of log-canonicity relevant to these stability conditions.

Findings

Extended Chow stability criteria to positive characteristics.

Proved stability of sums of Chow stable cycles.

Discussed properties of log-canonicity with examples.

Abstract

We extend two results on Chow (semi-)stability to positive characteristics. One is on the stability of non-singular projective hypersurfaces of degree greater than 2, and the other is the criterion by Y. Lee in terms of log canonical thresholds. Some properties of log-canonicity in positive characteristics are discussed with a couple of examples, in connection with the proof of the latter one. It is also proven in appendix that the sum of Chow (semi-)stable cycles are again Chow (semi-)stable.