F-signature of pairs and the asymptotic behavior of Frobenius splittings

2011/07/31 by Manuel Blickle, Karl Schwede, Kevin Tucker · 2 citations
Mathematics · #math.AC #math.AG #msc:13A35 #msc:13D40 #msc:14B05 #msc:13H10

paper · pdf

published as Adv. Math. 231 (2012), no. 6, 3232-3258 · 27 pages, exposition improved, typos corrected, references added. To appear in Advances in Mathematics

arxiv created 2012/09/07 · arxiv updated 2012/12/07

Abstract

We generalize F-signature to pairs (R,D) where D is a Cartier subalgebra on R as defined by the first two authors. In particular, we show the existence and positivity of the F-signature for any strongly F-regular pair. In one application, we answer an open question of I. Aberbach and F. Enescu by showing that the F-splitting ratio of an arbitrary F-pure local ring is strictly positive. Furthermore, we derive effective methods for computing the F-signature and the F-splitting ratio in the spirit of the work of R. Fedder.

Cited by

• Limit F -signature functions of two-variable binomial hypersurfaces
• Limit F-signature functions of two-variable binomial hypersurfaces

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