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arXiv · 1112.2423

F-purity versus log canonicity for polynomials

Daniel J. Hernández
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Abstract

In this article, we consider the conjectured relationship between F-purity and log canonicity for polynomials over the complex numbers. We associate to a collection M of n monomials a rational polytope P contained in [0,1]^n. Using P and the Newton polyhedron associated to M, we define a non-degeneracy condition under which log canonicity and dense F-pure type are equivalent for all linear combinations of the monomials in M. We also show that log canonicity corresponds to F-purity for very general polynomials. Our methods rely on showing that the F-pure and log canonical threshold agree for infinitely primes, and we accomplish this by comparing these thresholds with the thresholds associated to their monomial ideals.

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Daniel J. Hernández. 2011-12-12. F-purity versus log canonicity for polynomials. https://arxiv.org/abs/1112.2423

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