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- Steven B. Bradlow, Oscar García-Prada, Peter B. Gothen, Oscar Garćıa–Prada
- 2002

A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable holomorphic triples. In this paper we study non-emptiness, irreducibility, smoothness, and birational descriptions of… (More)

Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper we calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key… (More)

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor–Wood type inequality. Our main result is a count of the… (More)

- L. ÁLVAREZ-CÓNSUL, Oscar García-Prada
- 2005

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 in [1] and moduli spaces were constructed in [22, 24]. In this paper we study the variation of the moduli spaces with respect to… (More)

A good way to understand an object of study is, as Richard Feynman famously remarked, to “just look at the thing!”. In this paper we apply Feynman’s method to answer the following question: given a surface group representation in Sp(4,R), under what conditions can it be deformed to a representation which factors through a proper reductive subgroup of… (More)

- Oscar García-Prada, Daniel Hernández Ruipérez, Fabio Pioli, Carlos Prieto
- 2004

We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic equations on a triple — vortices — and… (More)

Using the L-norm of the Higgs field as a Morse function, we count the number of connected components of 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. This space is homeomorphic to the moduli space of representations of the… (More)

- Indranil Biswas, Oscar García-Prada, Jacques Hurtubise
- J. London Math. Society
- 2016

We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence between a certain deformation of the Hermitian-Einstein equations and our definition of stability for an extension. §

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