Criteria for very ampleness of rank two vector bundles over ruled surfaces

TL;DR

This paper establishes criteria for very ampleness of rank 2 vector bundles on ruled surfaces and applies these to resolve existence questions for certain low-degree threefolds.

Contribution

It provides new very ampleness criteria for rank 2 vector bundles over ruled surfaces, aiding in the classification of related threefolds.

Findings

Criteria for very ampleness over rational curves

Criteria for very ampleness over elliptic curves

Resolution of open existence questions for specific threefolds

Abstract

Very ampleness criteria for rank 2 vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.