Equimultiplicity in Hilbert–Kunz theory
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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.
KeywordsHilbert–Kunz multiplicity Tight closure Equimultiplicity
Mathematics Subject Classification13D40 13A35 13H15 14B05
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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