128 citations · 700 across the 44 of their papers we have counts for
10 papers · 1 filter
Gravitating vortices and Symplectic Reduction by Stages
L. Álvarez-Cónsul, M. Garcia-Fernandez, O. García-Prada +2
We undertake a novel approach to the existence problem for gravitating vortices on a Riemann surface based on symplectic reduction by stages, which seems to be new in the PDE as we…
Real Higgs pairs and Non-abelian Hodge correspondence on a Klein surface
Indranil Biswas, Luis Angel Calvo, Oscar Garcia-Prada
We introduce real structures on -twisted Higgs pairs over a compact Riemann surface equipped with an anti-holomorphic involution, and prove a Hitchin--Kobayashi correspondence f…
Maximal Higgs bundles for adjoint forms via Cayley correspondence
Oscar García-Prada, André Oliveira
For a fixed compact Riemann surface X, of genus at least 2, we count the number of connected components of the moduli space of maximal Higgs bundles over X for the hermitian groups…
Higgs bundles, the Toledo invariant and the Cayley correspondence
Olivier Biquard, Oscar Garcia-Prada, Roberto Rubio
We define the Toledo invariant of a G-Higgs bundle on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invari…
Parabolic Higgs bundles and representations of the fundamental group of a punctured surface into a real group
Olivier Biquard, Oscar Garcia-Prada, Ignasi Mundet i Riera
We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects a…
Gravitating vortices, cosmic strings, and the Kähler--Yang--Mills equations
Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada
In this paper we construct new solutions of the Kahler-Yang-Mills equations, by applying dimensional reduction methods to the product of the complex projective line with a compact…
A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space
Oscar Garcia-Prada, Domingo Toledo
We prove a Milnor-Wood inequality for representations of the fundamental group of a compact complex hyperbolic manifold in the group of isometries of quaternionic hyperbolic space.…
The Hitchin-Kobayashi correspondence, Higgs pairs and surface group representations
Oscar Garcia-Prada, Peter B. Gothen, Ignasi Mundet i Riera
We develop a complete Hitchin-Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability…
Relative Hitchin--Kobayashi correspondences for principal pairs
Steven B. Bradlow, Oscar Garcia-Prada, Ignasi Mundet i Rierra
A principal pair consists of a holomorphic principal -bundle together with a holomorphic section of an associated Kaehler fibration. Such objects support natural gauge theoretic…
Hitchin-Kobayashi correspondence, quivers, and vortices
Luis Álvarez-Cónsul, Oscar García-Prada
A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collec…