Bertini Theorems for $F$-signature and Hilbert-Kunz multiplicity

Abstract

We show that Bertini theorems hold for $F$-signature and Hilbert--Kunz multiplicity. In particular, if $X\subseteq {\mathbb{P}}^n$ is normal and quasi-projective with $F$-signature greater than $\lambda$ (respectively the Hilbert--Kunz multiplicity is less than $\lambda$) at all points $x\in X$, then for a general hyperplane $H\subseteq {\mathbb{P}}^n$ the $F$-signature (respectively Hilbert--Kunz multiplicity) of $X\cap H$ is greater than $\lambda$ (respectively less than $\lambda$) at all points $x\in X\cap H$.

23 pages, typos corrected and proofs improved, to appear in Math. Z

References in corpus (3)

• Two theorems about maximal Cohen--Macaulay modules
• F-signature and Hilbert-Kunz Multipicity: a combined approach and comparison
• Upper semi-continuity of the Hilbert-Kunz multiplicity

Cited by in corpus (1)

• Seshadri Constants and Fujita's Conjecture via Positive Characteristic Methods