2005/12/21 by Luis Álvarez-Cónsul, Luis Alvarez-Consul, Oscar Garcia-Prada +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG #math.DG #msc:14D20 #msc:14D21 #msc:32G13
paper · pdf · doi:10.1155/imrp/2006/73597
published as International Mathematics Research Papers, Volume 2006 (2006), Article ID 73597, 82 pages · 70 pages
arxiv created 2005/12/21 · openalex publication_date 2006/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study holomorphic (n + 1)-chains En → En−1 → ⋯ → E0 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 by the first two authors and moduli spaces were constructed by the third author. 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). 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.