O. García-Prada

activity

19942024

most citedMaximal surface group representations in isometry groups of classical Hermitian symmetric spaces

128 citations · 700 across the 44 of their papers we have counts for

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31 papers · 1 filter

math.AG2023

Vinberg pairs and Higgs bundles

Oscar García-Prada

We explore the role of Vinberg pairs defined by cyclic gradings of a semisimple complex Lie algebra in the context of Higgs bundle theory.

math.AG2023

Multiplicative Higgs bundles and involutions

Guillermo Gallego, Oscar Garcia-Prada

In this paper we generalize the theory of multiplicative $G$ -Higgs bundles over a curve to pairs $(G, θ)$ , where $G$ is a reductive algebraic group and $θ$ is an involution of $G$ .…

math.AG2021★ 3 cited

Higgs bundles twisted by a vector bundle

Guillermo Gallego, Oscar Garcia-Prada, M. S. Narasimhan

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle o…

math.AG2021★ 1 cited

Arakelov-Milnor inequalities and maximal variations of Hodge structure

Olivier Biquard, Brian Collier, Oscar Garcia-Prada +1

In this paper we study the $C^{*}$ -fixed points in moduli spaces of Higgs bundles over a compact Riemann surface for a complex semisimple Lie group and its real forms. These…

math.AG2021★ 5 cited

A general Cayley correspondence and higher Teichmüller spaces

Steve Bradlow, Brian Collier, Oscar Garcia-Prada +2

We introduce a new class of $sl_{2}$ -triples in a complex simple Lie algebra $g$ , which we call magical. Such an $sl_{2}$ -triple canonically defines a…

math.AG2018

Involutions of rank 2 Higgs bundle moduli spaces

Oscar Garcia-Prada, S. Ramanan

We consider the moduli space of rank 2 Higgs bundles with fixed determinant over a smooth projective curve X of genus 2 over the complex numbers, and study involutions defined by t…

math.AG2018★ 8 cited

Exotic components of $SO (p, q)$ surface group representations, and their Higgs bundle avatars

Marta Aparicio-Arroyo, Steven Bradlow, Brian Collier +3

For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topo…

math.AG2017

Higgs bundles, branes and Langlands duality

Indranil Biswas, Oscar García-Prada, Jacques Hurtubise

Given a compact Riemann surface $X$ and a complex reductive Lie group $G$ equipped with real structures, we define antiholomorphic involutions on the moduli space of $G$ -Higgs bund…

math.AG2017★ 9 cited

Irreducibility of moduli of semistable Chains and applications to U(p,q)-Higgs bundles

Steven Bradlow, Oscar Garcia-Prada, Peter Gothen +1

We give necessary and sufficient conditions for moduli spaces of semistable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components…

math.AG2016

Action of the mapping class group on character varieties and Higgs bundles

Oscar Garcia-Prada, Graeme Wilkin

We consider the action of a finite subgroup of the mapping class group $M o d (S)$ of an oriented compact surface $S$ of genus $g \geq 2$ on the moduli space $R (S, G)$ of rep…

math.AG2016★ 33 cited

Involutions and higher order automorphisms of Higgs bundle moduli spaces

Oscar Garcia-Prada, S. Ramanan

We consider the moduli space $M (G)$ of $G$ -Higgs bundles over a compact Riemann surface $X$ , where $G$ is a complex semisimple Lie group. This is a hyperkähler manifold h…

math.AG2016★ 2 cited

Higgs bundles over elliptic curves for real groups

Emilio Franco, Óscar García-Prada, P. E. Newstead

We study topologically trivial $G$ -Higgs bundles over an elliptic curve $X$ when the structure group $G$ is a connected real form of a complex semisimple Lie group $G^{C}$ …

math.AG2015★ 1 cited

Pseudo-real principal $G$ -bundles over a real curve

Indranil Biswas, Oscar Garcia-Prada, Jacques Hurtubise

We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixin…

math.AG2013★ 8 cited

Higgs bundles over elliptic curves for complex reductive Lie groups

Emilio Franco, Oscar Garcia-Prada, P. E. Newstead

We study Higgs bundles over an elliptic curve with complex reductive structure group, describing the (normalization of) its moduli spaces and the associated Hitchin fibration. The…

math.AG2013★ 11 cited

Higgs bundles for the non-compact dual of the special orthogonal group

Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen

Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group G. In this paper we examine the case G=SO*(2n). We describe a rigidity phenomenon enc…

math.AG2013★ 3 cited

Higgs bundles over elliptic curves

Emilio Franco, Oscar Garcia-Prada, P. E. Newstead

In this paper we study $G$ -Higgs bundles over an elliptic curve when the structure group $G$ is a classical complex reductive Lie group. Modifying the notion of family, we define a…

math.AG2012★ 3 cited

Pseudo-real principal Higgs bundles on compact Kaehler manifolds

Indranil Biswas, Oscar Garcia-Prada, Jacques Hurtubise

Let $X$ be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let $G$ be a connected complex reductive…

math.AG2012★ 29 cited

The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)

Oscar García-Prada, Jochen Heinloth

Building on our previous joint work with A. Schmitt [7] we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the co…

math.AG2010

Higgs bundles for the Lorentz group

Marta Aparicio Arroyo, Oscar Garcia-Prada

Using the Morse-theoretic methods introduced by Hitchin, we prove that the moduli space of $\SO_0(1,n)$-Higgs bundles when $n$ is odd has two connected components.

math.AG2009★ 46 cited

Deformations of maximal representations in Sp(4,R)

Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen

We use Higgs bundles to answer the following question: When can a maximal Sp(4,R)-representation of a surface group be deformed to a representation which factors through a proper r…

math.AG2008★ 62 cited

Higgs bundles and surface group representations in the real symplectic group

Oscar Garcia-Prada, Peter B. Gothen, Ignasi Mundet i Riera

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…

math.AG2007★ 1 cited

Moduli spaces of coherent systems of small slope on algebraic curves

S. B. Bradlow, O. Garcia-Prada, V. Mercat +2

Let $C$ be an algebraic curve of genus $g \geq 2$ . A coherent system on $C$ consists of a pair $(E, V)$ , where $E$ is an algebraic vector bundle over $C$ of rank $n$ and degree $d$ and…

math.AG2006

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

Oscar Garcia-Prada, Marina Logares, Vicente Muñoz

Using the $L^{2}$ -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 surf…

math.AG2005★ 32 cited

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

Luis Alvarez-Consul, Oscar Garcia-Prada, Alexander H. W. Schmitt

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 noti…