Rank two weak Fano bundles on del Pezzo threefolds of degree five

TL;DR

This paper classifies rank two weak Fano bundles on del Pezzo threefolds of degree five, analyzes their moduli spaces, and determines conditions for smoothness and irreducibility, also providing classifications on lower degree del Pezzo threefolds.

Contribution

It provides a complete classification of rank two weak Fano bundles on degree five del Pezzo threefolds and characterizes their moduli spaces, including splitting criteria on lower degree cases.

Findings

Classified rank two weak Fano bundles on degree five del Pezzo threefolds.

Determined when moduli spaces are smooth, irreducible, and fine.

Proved splitting of bundles on degree one or two del Pezzo threefolds.

Abstract

This paper classifies rank two vector bundles on a del Pezzo threefold $X$ of degree five whose projectivizations are weak Fano. This classification is then used to determine properties of the moduli spaces of such vector bundles on $X$, and we determine precisely when the moduli spaces are smooth, irreducible, and fine. We also prove that such a bundle on a del Pezzo threefold of degree one or two splits, and as result give a classification of weak Fano bundles of rank two on a del Pezzo threefold of Picard rank one.