Coherent Systems on Elliptic curves

2004/11/03 by Herbert Lange, H. Lange, Lange, H. +2 · 1 citation
Mathematics · #14F05 #14H60 #32L10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14F05 #msc:14H60 #msc:32L10

paper · pdf · doi:10.48550/arxiv.math/0411064

Final version with some improvements in the presentation and an additional reference

openalex publication_date 2004/11/03 · arxiv created 2005/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider coherent systems (E,V) on an elliptic curve which are stable with respect to some value of a parameter α. We show that the corresponding moduli spaces, if non-empty, are smooth and irreducible of the expected dimenson. Moreover we give precise conditions for non-emptiness of the moduli spaces. Finally we study the variation of the moduli spaces with α.

Cited by

• Derived category of coherent systems on curves and stability conditions

Related

• Coherent systems of genus 0
• Existence of coherent systems
• Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves
• Non-emptiness of moduli spaces of coherent systems
• Moduli spaces of coherent systems of small slope on algebraic curves