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

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

1992-03-19

arxiv.org/abs/alg-geom/9203004v1

Mathematics

Algebraic Geometry

34 pages, AmS-TeX 2.0

Scientific paper

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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