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

Abstract

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.

arXiv comment70 pages

References in corpus (5)

• Surface group representations in PU(p,q) and Higgs bundles
• Hitchin-Kobayashi correspondence, quivers, and vortices
• Homological algebra of twisted quiver bundles
• Moduli spaces of holomorphic triples over compact Riemann surfaces
• Global Boundedness for Decorated Sheaves

Cited by in corpus (15)

• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• Stratifications on the Moduli Space of Higgs Bundles
• Hilbert-Mumford stability on algebraic stacks and applications to $\mathcal{G}$-bundles on curves
• Aspects of the topology and combinatorics of Higgs bundle moduli spaces
• Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles
• Twisted argyle quivers and Higgs bundles
• Birationality of moduli spaces of twisted $\mathrm{U}(p,q)$-Higgs bundles
• Motives of moduli spaces of rank 3 vector bundles and Higgs bundles on a curve
• Simpson Filtration and Oper Stratum Conjecture
• Irreducible components of the global nilpotent cone
• The intersection form on moduli spaces of twisted PGL_n-Higgs bundles vanishes
• Hodge polynomials of the moduli spaces of triples of rank (2,2)
• Betti numbers of parabolic U(2,1)-Higgs bundles moduli spaces
• Tensor Products of Quiver Bundles
• Hitchin Pairs for non-compact real Lie groups