Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Higher rank prioritary bundles on ruled surfaces and their global sections

L. Costa, I. Macías Tarrío

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.

Higher rank prioritary bundles on ruled surfaces and their global sections

Abstract

Let be a ruled surface over a nonsingular curve of genus . The main goal of this paper is to construct simple prioritary vector bundles of any rank on and to give effective bounds for the dimension of their module of global sections.
Paper Structure (5 sections, 19 theorems, 133 equations)

This paper contains 5 sections, 19 theorems, 133 equations.

Table of Contents

  1. Introduction
  2. Preliminaries on prioritary sheaves
  3. Rank 3 prioritary bundles
  4. Rank 4 prioritary bundles
  5. Higher rank prioritary bundles

Key Result

Lemma 2.2

Let $X$ be a ruled surface over a nonsingular curve $C$ of genus $g\geq0$ and $D=aC_0+\mathfrak{b}f$ be a divisor on $X$ with $b:=\deg(\mathfrak{b})$. If $D$ is effective then $a,b\geq0$.

Theorems & Definitions (40)

  • Lemma 2.2
  • Proposition 2.3
  • Definition 2.4
  • Lemma 2.5
  • proof
  • Remark 2.6
  • Theorem 2.7
  • proof
  • Lemma 3.1
  • proof
  • ...and 30 more