$F$-PURITY VERSUS LOG CANONICITY FOR POLYNOMIALS. (23rd August 2016)

• Record Type: Journal Article
• Authors: HERNÁNDEZ, DANIEL J.
• Is Part Of: Nagoya mathematical journal. Volume 224(2016)
• Page Start: 10
• Page End: 36
• Publication Date: 2016-08-23
• Subjects: 13A35, -- 14B05; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1017/nmj.2016.14
• Languages: English
• ISSNs: 0027-7630

Abstract

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.