Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1077.14516
Demailly, Jean-Pierre; Ein, Lawrence; Lazarsfeld, Robert
A subadditivity property of multiplier ideals. (English)
[J] Mich. Math. J. 48, Spec. Vol., 137-156 (2000). ISSN 0026-2285

Summary: Given an effective $\bbfQ$-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 $\bbfQ$-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 {\it T. Fujita} [Kodai Math. J. 17, No. 1, 1--3 (1994; Zbl 0814.14006)] 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.

MSC 2000:: *14E99 Mappings and correspondences
14J17 Singularities of surfaces

Citations: Zbl 0814.14006

Cited in: Zbl 1180.13005 Zbl 1146.14003 Zbl 1102.13004 Zbl 1028.13003

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]