2011/12/12 by Daniel J. Hernández, Hernández, Daniel J. · 1 citation
Computer Science · Mathematics · #13A35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1112.2423
openalex publication_date 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.