Monads and Vector Bundles on Quadrics

TL;DR

This paper enhances the splitting criterion for vector bundles on quadrics, classifies certain rank 2 bundles without inner cohomology, and finds a surprising agreement with Fano bundle classifications.

Contribution

It improves Ottaviani's splitting criterion and provides a classification of rank 2 bundles on quadrics, aligning with known Fano bundle classifications.

Findings

Improved splitting criterion for vector bundles on quadrics

Classification of rank 2 bundles without inner cohomology on Q_n

Alignment with Fano bundle classifications

Abstract

We improve Ottaviani's splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without "inner" cohomology on Q_n (n>3). It surprisingly exactly agrees with the classification by Ancona, Peternell and Wisniewski of rank 2 Fano bundles.