Strong Watanabe-Yoshida conjecture for Complete Intersections

TL;DR

This paper proves the strong Watanabe-Yoshida conjecture for complete intersection singularities across all positive characteristics, and explicitly computes Hilbert-Kunz functions for specific singularities in low characteristics.

Contribution

It establishes the conjecture's validity for all positive characteristics and provides explicit computations for A1 and A2 singularities in characteristics 2 and 3.

Findings

Proof of the strong Watanabe-Yoshida conjecture for complete intersections in all positive characteristics.

Explicit Hilbert-Kunz function calculations for A1 and A2 singularities in characteristics 2 and 3.

Abstract

In this paper, we prove the strong form of the Watanabe-Yoshida conjecture for complete intersection singularities in every positive characteristic. In characteristics 2 and 3, we explicitly compute the Hilbert-Kunz functions of the A1 and A2 singularities.