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Equimultiplicity in Hilbert–Kunz theory

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Abstract

We study further the properties of Hilbert–Kunz multiplicity as a measure of singularity. This paper develops a theory of equimultiplicity for Hilbert–Kunz multiplicity and applies it to study the behavior of Hilbert–Kunz multiplicity on the Brenner–Monsky hypersurface. A number of applications follows, in particular we show that Hilbert–Kunz multiplicity attains infinitely many values and that equimultiple strata may not be locally closed.

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Notes

  1. Neil Epstein informed me that a more general change of limits formula was independently obtained in his joint work with Yongwei Yao.

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Acknowledgements

The results of this paper are a part of the author’s thesis written under Craig Huneke in the University of Virginia. I am indebted to Craig for his support and guidance. This project would not be possible without his constant encouragement. I also want to thank Mel Hochster and the anonymous referee who carefully read and helped to improve this manuscript.

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  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Ilya Smirnov

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  1. Ilya Smirnov
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Correspondence to Ilya Smirnov.

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Dedicated to Craig Huneke on the occasion of his 65th Birthday.

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Smirnov, I. Equimultiplicity in Hilbert–Kunz theory. Math. Z. 291, 245–278 (2019). https://doi.org/10.1007/s00209-018-2082-5

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  • DOI: https://doi.org/10.1007/s00209-018-2082-5

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