2012/07/04 by Wenbo Niu, Niu, Wenbo
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.1207.1082
21 pages, all comments welcome
openalex publication_date 2012/07/04 · arxiv created 2013/06/18 · arxiv updated 2013/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Y be a generic link of a subvariety X of a nonsingular variety A. We give a description of the Grauert-Riemenschneider canonical sheaf of Y in terms of the multiplier ideal sheaves associated to X and use it to study the singularities of Y. As the first application, we give a criterion when Y has rational singularities and show that log canonical threshold increases and log canonical pairs are preserved in generic linkage. As another application we give a quick and simple liaison method to generalize the results of de Fernex-Ein and Chardin-Ulrich on the Castelnuovo-Mumford regularity bound for a projective variety.