Hilbert–Kunz multiplicity and F ‐signature can disagree
Abstract
Abstract We compute the ‐signature function of the ample cone of any nontrivial ruled surface over , where is an algebraically closed field of prime characteristic. As an application, we construct a Noetherian ‐finite strongly ‐regular ring of prime characteristic admitting two maximal ideals at which the Hilbert–Kunz multiplicity and ‐signature measure different singularities; that is, and . Our calculation of the ‐signature for the Hirzebruch surfaces also corrects an inaccuracy in a preprint by other authors.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Rings
Modules
and Algebras
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 3
- Publication date
- 25 February 2026
- Language
- EN