21 citations · 119 across the 19 of their papers we have counts for
18 papers · 1 filter
Zero velocity Lagrangians in the Hitchin system
Peter Gothen, André Oliveira, Rodrigo Pereira
Lagrangians of the moduli space of Higgs bundles are a fundamental piece of its study under the lens of mirror symmetry. We construct a new class of Lagrangians defined via a zero…
Narasimhan--Ramanan branes and wobbly Higgs bundles
Emilio Franco, Peter B. Gothen, André G. Oliveira +1
Narasimhan--Ramanan branes were introduced by the authors in a previous article. They consist of a family of -branes inside the moduli space of Higgs bundles, and a family of…
Lie algebroid connections, twisted Higgs bundles and motives of moduli spaces
David Alfaya, André Oliveira
Let be an algebraic Lie algebroid over a smooth projective curve of genus such that is a line bundle whose degree is less than…
A general Cayley correspondence and higher Teichmüller spaces
Steve Bradlow, Brian Collier, Oscar Garcia-Prada +2
We introduce a new class of -triples in a complex simple Lie algebra , which we call magical. Such an -triple canonically defines a…
SO(p,q)-Higgs bundles and higher Teichmüller components
Marta Aparicio-Arroyo, Steven Bradlow, Brian Collier +3
Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others a…
Unramified covers and branes on the Hitchin system
Emilio Franco, Peter Gothen, André Oliveira +1
We study the locus of the moduli space of Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under an unramified cover. We equip these loci with a hyperh…
Exotic components of 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…
Topological mirror symmetry for parabolic Higgs bundles
Peter B. Gothen, André G. Oliveira
We prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli space of strongly parabolic Higgs bundles of rank two or three, with full flags. Although the…
Quadric bundles and their moduli spaces
André Oliveira
Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of in Sp(2n,R). We pro…
Quadric bundles applied to non-maximal Higgs bundles
André Oliveira
We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur…
Connectedness of Higgs bundle moduli for complex reductive Lie groups
Oscar García-Prada, André Oliveira
We carry an intrinsic approach to the study of the connectedness of the moduli space of -Higgs bundles, over a compact Riemann surface, when is a complex red…
Connectedness of the moduli of Sp(2p,2q)-Higgs bundles
Oscar García-Prada, André Oliveira
Using the Morse-theoretic techniques introduced by Hitchin, we prove that the moduli space of $\Sp(2p,2q)$-Higgs bundles over a compact Riemann surface of genus is connec…
Motives and the Hodge Conjecture for moduli spaces of pairs
Vicente Muñoz, André Oliveira, Jonathan Sánchez
Let be a smooth projective curve of genus over . Fix , . A pair over consists of an algebraic vector bundle of r…
Torelli theorem for the moduli spaces of rank 2 quadratic pairs
A. Oliveira
Let be a smooth projective complex curve. We prove that a Torelli type theorem holds, under certain conditions, for the moduli space of -polystable quadratic pairs on of…
Rank two quadratic pairs and surface group representations
Peter B. Gothen, André Oliveira
Let be a compact Riemann surface. A quadratic pair on consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that th…
The singular fibre of the Hitchin map
Peter B. Gothen, André Oliveira
Given any line bundle L of positive degree, on a compact Riemann surface, let be the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant isomorphic to $Λ…
Higgs bundles for the non-compact dual of the unitary group
Oscar García-Prada, André Oliveira
Using Morse-theoretic techniques, we show that the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface is connected.
Representations of surface groups in the projective general linear group
André Oliveira
Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We deter…