$F$-PURITY VERSUS LOG CANONICITY FOR POLYNOMIALS. (23rd August 2016) - HERNÁNDEZ, DANIEL J.
Abstract : In this article, we consider the conjectured relationship between $F$ -purity and log canonicity for polynomials over $\mathbb{C}$ . In particular, we show that log canonicity corresponds to dense $F$ -pure type for all polynomials whose supporting monomials satisfy a certain nondegeneracy condition. We also show that log canonicity corresponds to dense $F$ -pure type for very general polynomials over $\mathbb{C}$ . Our methods rely on showing that the $F$ -pure and log canonical thresholds agree for infinitely many primes, and we accomplish this by comparing these thresholds with the thresholds associated to their monomial term ideals.