Extension of holomorphic functions defined on non reduced analytic subvarieties

Abstract

The goal of this contribution is to investigate L${}^2$ extension properties for holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi extension theorem, we obtain several new surjectivity results for the restriction morphism to a non necessarily reduced subvariety, provided the latter is defined as the zero variety of a multiplier ideal sheaf. These extension results come with precise L${}^2$ estimates and (probably) optimal curvature conditions.

The legacy of Bernhard Riemann after one hundred and fifty years, 2015

References in corpus (2)

• Strong openness conjecture for plurisubharmonic functions
• A proof of the Ohsawa-Takegoshi theorem with sharp estimates

Cited by in corpus (16)

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• On weighted Bergman spaces of a domain with Levi-flat boundary
• Multiplier ideal sheaves, jumping numbers, and the restriction formula
• On an $L^2$ extension theorem from log-canonical centres with log-canonical measures
• Extension of cohomology classes and holomorphic sections defined on subvarieties
• On the minimal model program for projective varieties with pseudo-effective tangent sheaf
• Log canonical thresholds and Monge-Ampere masses
• Concavity of minimal $L^2$ integrals related to multipler ideal sheaves
• Boundary asymptotics of the relative Bergman kernel metric for curves
• Open problems in pluripotential theory
• On the extension of holomorphic sections from reduced unions of strata of divisors
• Semiclassical Ohsawa-Takegoshi extension theorem and asymptotics of the orthogonal Bergman kernel
• Global pluripotential theory on hybrid spaces
• Extension from lc centres and the extension theorem of Demailly but with estimates
• Multiplier ideal sheaves, complex singularity exponents, and restriction formula
• A note on multiplier ideal sheaves on complex spaces with singularities