Strong Watanabe-Yoshida conjecture for Complete Intersections
Commutative Algebra
2025-11-17 v3 Algebraic Geometry
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.
Cite
@article{arxiv.2506.09019,
title = {Strong Watanabe-Yoshida conjecture for Complete Intersections},
author = {Joel Castillo-Rey},
journal= {arXiv preprint arXiv:2506.09019},
year = {2025}
}
Comments
36 pages; v2: minor changes; v3: addition of Theorem 4.11, which fixes a gap in the previous version; added Theorem 1.23 (Han-Monsky algorithm) for reference; lots of minor changes and added remarks to improve exposition. Comments are very welcome!