A subadditivity property of multiplier ideals.
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Publication:5954555
DOI10.1307/MMJ/1030132712zbMATH Open1077.14516arXivmath/0002035OpenAlexW2005537290WikidataQ102077903 ScholiaQ102077903MaRDI QIDQ5954555
Author name not available (Why is that?)
Publication date: 4 February 2002
Published in: (Search for Journal in Brave)
Abstract: Given an effective Q-divisor D on a smooth complex variety, one can associate to D its multiplier ideal sheaf J(D), which measures in a somewhat subtle way the singularities of D. Because of their strong vanishing properties, these ideals have come to play an increasingly important role in higher dimensional geometry. We prove that for two effective Q-divisors D and E, one has the "subadditivity" relation: J(D + E) subseteq J(D) . J(E) . (We also establish several natural variants, including the analogous statement for the analytic multiplier ideals associated to plurisubharmonic functions.) As an application, we give a new proof of a theorem of Fujita concerning the volume of a big linear series on a projective variety. The first section of the paper contains an overview of the construction and basic properties of multiplier ideals from an algebro-geometric perspective, as well as a discussion of the relation between some asymptotic algebraic constructions and their analytic counterparts.
Full work available at URL: https://arxiv.org/abs/math/0002035
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