A remark by Daniel Ferrand on bundles on Fano threefolds

TL;DR

This paper classifies certain rank two vector bundles on Fano threefolds with specific stability, Chern class, and cohomological properties, contributing to the understanding of vector bundles on these varieties.

Contribution

It provides a classification of $ ext{mu}$-semistable rank two bundles with zero first Chern class and particular cohomological conditions on Fano threefolds.

Findings

Classification of specific rank two bundles on Fano threefolds.

Identification of conditions under which these bundles exist.

Insights into the structure of vector bundles with given stability and cohomology.

Abstract

Let $X$ be a Fano threefold with index $i_X$ and fundamental line bundle $\mathcal O_X(h)$. We classify $\mu$-semistable rank two bundles $\mathcal E$ on $X$ with $c_1(\mathcal E)=0$, $h^0(\mathcal E) \ne 0$ and $h^1(\mathcal E(-\lceil\frac{i_X}{2}\rceil h))=0$.