On the Abel-Jacobi Map for Divisors of Higher Rank on a Curve

1992/03/19 by Emili Bifet, Bifet, Emili, Franco Ghione +3 · 1 citation
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Pharmacological Effects of Natural Compounds

paper · pdf · doi:10.48550/arxiv.alg-geom/9203004

openalex publication_date 1992/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to present an algebro-geometric approach to the study of the geometry of the moduli space of stable bundles on a smooth projective curve defined over an algebraically closed field k, of arbitrary characteristic. This establishes a bridge between the arithmetic approach of Harder, Narasimhan et al. and the gauge group approach of Atiyah and Bott. One of the basic ideas is to consider a notion of divisor of higher rank and a suitable Abel-Jacobi map generalizing the classical notions in rank one.

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• Isomorphisms between moduli stacks of vector bundles with fixed determinant

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