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arXiv · 2210.00566

The F-signature Function on the Ample Cone

Seungsu Lee·Suchitra Pande
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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.

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Seungsu Lee, Suchitra Pande. 2022-10-02. The F-signature Function on the Ample Cone. https://doi.org/10.1093/imrn%2Frnad174

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