Extension of Twisted Pluricanonical Sections with Plurisubharmonic Weight and Invariance of Semipositively Twisted Plurigenera for Manifolds Not Necessarily of General Type

By Y. Siu. 2002

228 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7b8e82cdeb546e13e39fda7b667f8adbc1fd7892

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Extension theorems, non-vanishing and the existence of good minimal models (2010, methodology): “In this last part of the proof of (1.7), we first recall that by the techniques originating in Siu’s seminal article [Siu00], for any fixed section sA ∈ H0(X,OX(A)), the section u⊗k ⊗ sA extends to X , for any k ≥ 1, (cf. [HM10, 6.3]).”
Complex surfaces of general type: some recent progress (2006, methodology): “The Kodaira dimension is invariant under deformation (by Siu’s theorem [Siu02], generalizing Iitaka’s theorem for surfaces) and can assume the values −∞, 0, . . . , n = dimX .”
Curvature of vector bundles associated to holomorphic fibrations (2005, background): “See also [27] fo r a closely related result.”
Bergman kernels and the pseudoeffectivity of relative canonical bundles (2007, background): “Siu to prove the invariance of plurigenera, see [31], [32].”
A solution of an $L^{2}$ extension problem with optimal estimate and applications (2013, background): “M is a projective family (see [51]), and S is any closed complex subvariety of M .”
Positivity of twisted relative pluricanonical bundles and their direct images (2014, background): “For example, if h is continuous, or more generally the multiplier ideal I(hy) = OXy on Xy with y ∈ Y0 for any integer k > 0, the invariance of plurigenera [41] and [38] verify this.”
Effectiveness of Demailly’s strong openness conjecture and related problems (2014, unknown): “Background of L2 method can referred to [8], [16], [17], [18], [22], [34], [35], [39], [40], [43], etc.”