On the obstruction to extending a vector bundle from a submanifold

TL;DR

This paper provides an explicit formula for the first obstruction to extending a holomorphic vector bundle from a submanifold, using the Atiyah class, clarifying a classical problem in complex geometry.

Contribution

It introduces a concrete formula for the first obstruction to extension, linking Griffiths' classical obstruction to the Atiyah class of the bundle.

Findings

Explicit formula for the first obstruction in terms of the Atiyah class

Clarification of the relationship between Griffiths' obstruction and the Atiyah class

Enhanced understanding of extension problems for holomorphic vector bundles

Abstract

For the first obstruction to extending a holomorphic vector bundle from a submanifold of a complex manifold found by Griffiths we give an explicit formula in terms of the Atiyah class of the bundle.