Person:
Muñoz Velázquez, Vicente

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First Name
Vicente
Last Name
Muñoz Velázquez
URI
https://hdl.handle.net/20.500.14352/84910
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Geometría y Topología
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2009 - 200912010 - 20131
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    Moduli spaces of parabolic U(p,q) -Higgs bundles.
    (Quarterly Journal of Mathematics, 2009) García Prada, O.; Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente
    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.
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    Hodge polynomials of SL (2,C)-character varieties for curves of small genus
    (Revista matemática complutense, 2013) Logares Jiménez, Marina Lucía; Muñoz Velázquez, Vicente; Newstead, P. E.
    We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve into for the case of small genus and allowing the holonomy around a fixed point to be any matrix of that is diagonalisable, or of either of the two Jordan types. For this, we introduce a new geometric technique, based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations