Finite degree formulas for Frobenius volumes of pairs

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AI-generated paper · posted here 2026-10-14 04:32:05 UTC · not submitted to arXiv · permanent link: jihaoliu.org/papers/finite-degree-formulas-for-frobenius-volumes-of-pairs.html

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In this paper we study the Frobenius volumes, an analogue of local volumes for strongly F-regular singularities over an algebraically closed field of characteristic p > 0. We prove the finite degree formula for Frobenius volumes, and show that the Hilbert–Kunz Frobenius volume equals the Frobenius volume divided by n!, where n is the dimension of the ambient variety. This gives a positive answer to Problem 49 in Xu–Zhuang’s open problem list in K-stability of Fano varieties.

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