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Moduli spaces of parabolic U(p,q) -Higgs bundles.

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García Prada, O. and Logares, M. and Muñoz, Vicente (2009) Moduli spaces of parabolic U(p,q) -Higgs bundles. Quarterly Journal of Mathematics , 60 (2). pp. 183-233. ISSN 0033-5606

Official URL: http://qjmath.oxfordjournals.org/content/60/2/183



Abstract

Using the L2-norm of the Higgs field as a Morse function, we study the moduli space of parabolic U(p, q)-Higgs bundles over a Riemann surface with a finite number of marked points, under certain genericity conditions on the parabolic structure. When the parabolic degree is zero this space is homeomorphic to the moduli space of representations of the fundamental group of the punctured surface in U(p, q), with fixed compact holonomy classes around the marked points. By means of this homeomorphism we count the number of connected components of this moduli space of representations. Finally, we apply our results to the study of representations of the fundamental group of elliptic surfaces of general type.


Item Type:Article
Subjects:Sciences > Mathematics > Geometry
ID Code:21310
Deposited On:10 May 2013 10:18
Last Modified:12 Dec 2018 15:13

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