The F-signature Function on the Ample Cone

Abstract

For any fixed globally F-regular projective variety X over an algebraically closed field of positive characteristic, we study the F-signature of section rings of X with respect to the ample Cartier divisors on X. In particular, we define an F-signature function on the ample cone of X and show that it is locally Lipschitz continuous. We further prove that the F-signature function extends to the boundary of the ample cone. We also establish an effective comparison between the F-signature function and the volume function on the ample cone. As a consequence, we show that for divisors that are nef but not big, the extension of the F-signature is zero.

30 pages, 1 figure, Final version, Appeared in IMRN

References in corpus (8)

• Globally $F$-regular and log Fano varieties
• Two theorems about maximal Cohen--Macaulay modules
• F-signature exists
• Boundedness of pluricanonical maps of varieties of general type
• Fundamental groups of $F$-regular singularities via $F$-signature
• The number of torsion divisors in a strongly $F$-regular ring is bounded by the reciprocal of $F$-signature
• $F$-signature under birational morphisms
• Korff $F$-signatures of Hirzebruch surfaces

Cited by in corpus (1)

• On tame ramification and centers of $F$-purity