Second Infintesimal Neighborhoods of Projective Bundle Sections

TL;DR

This paper demonstrates that a projective bundle with a section can be uniquely reconstructed from the second infinitesimal neighborhood of that section, revealing a new way to understand the bundle's structure.

Contribution

It introduces a novel method to recover a projective bundle from the embedding of its section's second infinitesimal neighborhood.

Findings

Unique recovery of projective bundles from second infinitesimal neighborhoods

New insights into the local structure of projective bundles

Potential applications in bundle classification

Abstract

This short paper shows that a projective bundle over a smooth variety with a section can be uniquely recovered from the embedding of the section in its second infinitesimal neighborhood within the bundle.