Log Canonical Thresholds for Plane Curves in Arbitrary Characteristic

TL;DR

This paper extends the formula for log canonical thresholds of plane curves from complex numbers to arbitrary characteristic fields, using valuation theory instead of D-module theory.

Contribution

It provides a new proof of the LCT formula applicable in any characteristic, broadening the understanding of singularities in algebraic geometry.

Findings

LCT formula generalized to arbitrary characteristic

Proof relies solely on valuation theory

Applicable to a wider class of algebraic curves

Abstract

We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.