On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces

Details On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces On the geometry of moduli spaces of holomorphic chains over compact Riemann surfaces

2005-12-21

arxiv.org/abs/math/0512498v1

International Mathematics Research Papers, Volume 2006 (2006), Article ID 73597, 82 pages

Mathematics

Algebraic Geometry

70 pages

Scientific paper

10.1155/IMRP/2006/73597

We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was introduced in the work of the first two authors and moduli spaces were constructed by the third one. In this paper we study the variation of the moduli spaces with respect to the stability parameters. In particular we characterize a parameter region where the moduli spaces are birationally equivalent. A detailed study is given for the case of 3-chains, generalizing that of 2-chains (triples) in the work of Bradlow, Garcia-Prada and Gothen. Our work is motivated by the study of the topology of moduli spaces of Higgs bundles and their relation to representations of the fundamental group of the surface.

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