A subadditivity property of multiplier ideals.

By J. Demailly, L. Ein, R. Lazarsfeld. 2000

228 citations recorded by the source corpus.

Let X be a smooth complex quasi-projective variety, and let D be an effective Q-divisor on X. One can associate to D its multiplier ideal sheaf J (D) = J (X,D) ⊆ OX , whose zeroes are supported on the locus at which the pair (X,D) fails to have log-terminal singularities. It is useful to think of J (D) as reflecting in a somewhat subtle way the singularities of D: the “worse” the singularities, the smaller the ideal. These ideals and their variants have come to play an increasingly important role in higher dimensional geometry, largely because of their strong vanishing properties. Among the papers in which they figure prominently, we might mention for instance [30], [4], [33], [2], [13], [34], [19], [14] and [8]. See [6] for a survey.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bd8a21a141a877b7fbdd349b30f5974664ff0082

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Citations in the corpus

Valuations and multiplier ideals (2004, methodology): “2 ), which holds by [ DEL ] (see the proof of Lemma 8.8).”
Uniform approximation of Abhyankar valuation ideals in smooth function fields (2002, unknown): “Among the various properties these ideals satisfy, we will need three in This is established in [6] using vanishing theorems.”
An algebraic approach to the openness conjecture of Demailly and Kollár (2012, methodology): “at a point xon a complex manifold with := c x(’) < 1. To ’we associate a sequence b = (b j) j1 of ideals by letting b j be the analytic multiplier ideal of the psh function j’. It follows from [DEL00] that b is subadditive. Further, using techniques due to Demailly [Dem92, Dem93], one can show t”
Toric plurisubharmonic functions and analytic adjoint ideal sheaves (2010, background): “We need to recall the definition of a right-regularized version of the multiplier ideal sheaf I(φ), introduced in [3]:”
On the Cohomology of Pseudoeffective Line Bundles (2014, background): “functions ϕm produced by Th. 1.2 do not in general satisfy ϕm+1 < ϕm, in other words their singularities may not always increase monotonically to those of ϕ. Thanks to the subbadditivity result of [DEL00], this is however the case for any subsequence ϕm k such that mk divides mk+1, e.g. mk = 2k o”