On divisors computing MLD's and LCT's

2016/05/31 by Harold Blum, Blum, Harold · 1 citation
Computer Science · Mathematics · #14B05 #14E30 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1605.09662

openalex publication_date 2016/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the graded sequence of ideals associated to a divisor over a variety. We systematically study this invariant and also prove a result describing which divisors compute asymptotic log canonical thresholds.

Cited by

• Optimal bounds for local volumes of threefold singularities

Related

• A finiteness property of graded sequences of ideals
• Upper bound of discrepancies of divisors computing minimal log discrepancies on surfaces
• Variation of log canonical thresholds in linear systems
• Mld's vs thresholds and flips
• Liftings of ideals in positive characteristic to those in characteristic zero : Low dimension