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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 245–278 | Cite as

Equimultiplicity in Hilbert–Kunz theory

  • Ilya SmirnovEmail author
Article
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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.

Keywords

Hilbert–Kunz multiplicity Tight closure Equimultiplicity 

Mathematics Subject Classification

13D40 13A35 13H15 14B05 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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