Joel Castillo : The Strong Watanabe–Yoshida conjecture for complete intersections

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Nov. 17, 2025, 3 p.m.

In

636 SEO

Abstract

The Watanabe–Yoshida conjecture states that the Hilbert–Kunz multiplicity attains its minimal value across singularities exactly at quadric hypersurfaces. It further claims that these are characterised by this property, but this part of the conjecture remained largely unaddressed in the literature. We present an affirmative answer to this problem for complete intersections in every positive characteristic, improving a theorem by Enescu and Shimomoto, thus settling the conjecture for this family of singularities. The proof relies on advanced characteristic-dependent applications of a technique developed by Han and Monsky, and critically includes a explicit calculation needed to fill the gaps for the often-overlooked characteristic 2 case.