On the extension of holomorphic sections from reduced unions of strata of divisors

TL;DR

This paper proves an extension theorem for holomorphic sections from unions of divisor strata, leading to new results on extension properties and global generation of vector bundles.

Contribution

It introduces a new extension theorem of Ohsawa--Takegoshi type for unions of divisor strata, advancing understanding of holomorphic section extension.

Findings

Extension theorem for unions of divisor strata established

Results on extension from snc divisors derived

Generic global generation of vector bundles demonstrated

Abstract

In this paper we study the problem of extension of holomorphic sections of line bundles/vector bundles from reduced unions of strata of divisors. An extension theorem of Ohsawa--Takegoshi type is proved. As consequences we deduce several qualitative results on extension from snc divisors and generic global generation of vector bundles.