Higher rank prioritary bundles on ruled surfaces and their global sections

TL;DR

This paper constructs simple prioritary vector bundles of any rank on ruled surfaces over curves and provides bounds for the dimension of their global sections.

Contribution

It introduces a method to construct prioritary bundles of arbitrary rank on ruled surfaces and estimates their global sections' dimension.

Findings

Construction of prioritary bundles of any rank on ruled surfaces.

Effective bounds for the dimension of global sections.

Abstract

Let $X$ be a ruled surface over a nonsingular curve $C$ of genus $g\geq0$. The main goal of this paper is to construct simple prioritary vector bundles of any rank $r$ on $X$ and to give effective bounds for the dimension of their module of global sections.