Identifying quadric bundle structures on complex projective varieties

TL;DR

This paper characterizes smooth complex projective varieties with quadric bundle structures using the geometry of rational curves, providing new insights into their classification.

Contribution

It offers a novel characterization of varieties admitting quadric bundle structures based on rational curve families.

Findings

Characterization of varieties with quadric bundle structures

Connection between rational curves and bundle geometry

New criteria for identifying quadric bundles

Abstract

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.