On neighborhoods of projective space bundles over elliptic curves

TL;DR

This paper establishes conditions under which neighborhoods of projective space bundles over elliptic curves are holomorphically equivalent to neighborhoods of their normal bundle's zero section, aiding understanding of local geometric structures.

Contribution

It provides new criteria for the local equivalence of neighborhoods in complex geometry, specifically for projective space bundles over elliptic curves.

Findings

Neighborhoods are holomorphically equivalent under certain conditions.

Criteria relate to the structure of the normal bundle.

Results improve understanding of local geometry around such bundles.

Abstract

We give conditions ensuring that a neighborhood of an embedded projective space bundle over an elliptic curve is holomorphically equivalent to a neighborhood of the zero section of its normal bundle.