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Hilbert-Kunz multiplicity of quadrics via Ehrhart theory
Igor Pak, Boris Shapiro, Ilya Smirnov +1
We show that the Hilbert-Kunz multiplicity of the d-dimensional non-degenerate quadric hypersurface of characteristic p > 2 is a rational function of p composed from the Ehrhart po…
F-singularities of polynomials with square-free support
Aldo Conca, Alessandro De Stefani, Luis Núñez-Betancourt +1
We show that the intersection of the irreducible components of a hypersurface defined by a polynomial with square-free support has F-rational singularities in characteristic .…
The defect of the F-pure threshold
Alessandro De Stefani, Luis Núñez-Betancourt, Ilya Smirnov
Introduced by Takagi and Watanabe, the F-pure threshold is an invariant defined in terms of the Frobenius homomorphism. While it finds applications in various settings, it is prima…
Tight closure of products and F-rational singularities
Alessandro De Stefani, Ilya Smirnov
We prove a characterization of F-rationality in terms of tight closure of products of parameter ideals. Our results are inspired by the theory of complete ideals for surfaces and,…