Extension of holomorphic functions defined on non reduced analytic subvarieties

TL;DR

This paper investigates L^2 extension properties for holomorphic sections of vector bundles on non-reduced analytic subvarieties, providing new surjectivity results with precise estimates and optimal curvature conditions.

Contribution

It extends the Ohsawa-Takegoshi theorem techniques to non-reduced subvarieties, establishing new L^2 extension results with sharp estimates.

Findings

New surjectivity results for restriction morphisms

L^2 extension theorems with optimal curvature conditions

Extension results applicable to non-reduced 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.