Verlinde bundles and generalized theta linear series

TL;DR

This paper investigates the properties of generalized theta linear series on moduli spaces of vector bundles on curves using Verlinde bundles and abelian variety techniques to understand duality and generation properties.

Contribution

It introduces a novel approach using Verlinde bundles and abelian varieties to analyze theta linear series on moduli spaces, revealing new duality and generation insights.

Findings

Establishes duality relations between theta functions.

Provides conditions for global generation of theta linear series.

Enhances understanding of the structure of moduli spaces.

Abstract

In this paper we approach the study of generalized theta linear series on moduli of vector bundles on curves via vector bundle techniques on abelian varieties. We study what are called the Verlinde bundles in order to obtain information about duality between theta functions and effective global and normal generation on these moduli spaces.