13 citations · 58 across the 18 of their papers we have counts for
18 papers · 1 filter
Motive of the representation varieties of torus knots for low rank affine groups
Ángel González-Prieto, Marina Logares, Vicente Muñoz
We compute the motive of the variety of representations of the torus knot of type (m,n) into the affine groups and . For this, we stratify the varieties and sh…
On character varieties of singular manifolds
Ángel González-Prieto, Marina Logares
In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of -representation va…
Representation variety for the rank one affine group
Angel González-Prieto, Marina Logares, Vicente Muñoz
The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different a…
Moduli spaces of framed --Higgs bundles and symplectic geometry
Indranil Biswas, Marina Logares, Ana Peón-Nieto
Let be a compact connected Riemann surface, a reduced effective divisor, a connected complex reductive affine algebraic group and …
On Higgs Bundles on Nodal Curves
Marina Logares
This is a review article on some applications of generalised parabolic structures to the study of torsion free sheaves and -twisted Hitchin pairs on nodal curves. In particular,…
Symplectic geometry of a moduli space of framed Higgs bundles
Indranil Biswas, Marina Logares, Ana Peón-Nieto
Let be a compact connected Riemann surface and an effective divisor on . Let denote the moduli space of -twisted stable Higgs bundles (a special…
A lax monoidal Topological Quantum Field Theory for representation varieties
Ángel González-Prieto, Marina Logares, Vicente Muñoz
We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-Hodge polynomials of representation varieties of the fundamental group of any closed manifold int…
Integrable systems and Torelli theorems for the moduli spaces of parabolic bundles and parabolic Higgs bundles
Indranil Biswas, Tomás L. Gómez, Marina Logares
We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weigh…
Bohr--Sommerfeld Lagrangians of moduli spaces of Higgs bundles
Indranil Biswas, Niels Leth Gammelgaard, Marina Logares
Let be a compact connected Riemann surface of genus at least two. Let denote the moduli space of semistable Higgs bundles on of rank and degree . We prove…
Hodge polynomials of the SL(2,C)-character variety of an elliptic curve with two marked points
Marina Logares, Vicente Muñoz
We compute the Hodge polynomials for the moduli space of representations of an elliptic curve with two marked points into SL(2,C). When we fix the conjugacy classes of the represen…
The Topology of Parabolic Character Varieties of Free Groups
Indranil Biswas, Carlos Florentino, Sean Lawton +1
Let G be a complex affine algebraic reductive group, and let K be a maximal compact subgroup of G. Fix elements h_1,...,h_m in K. For n greater than or equal to 0, let X (respectiv…
Hodge-Deligne polynomials of SL(2,C)-character varieties for curves of small genus
Marina Logares, Vicente Muñoz, Peter E. Newstead
We compute the Hodge-Deligne polynomials of the moduli spaces of representations of the fundamental group of a complex surface into SL(2,C), for the case of small genus g, and allo…
Brauer group of moduli spaces of pairs
Indranil Biswas, Marina Logares, Vicente Muñoz
We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.
On moduli spaces of Hitchin pairs
Indranil Biswas, Peter B. Gothen, Marina Logares
Let be a compact Riemann surface of genus at--least two. Fix a holomorphic line bundle over . Let be the moduli space of Hitchin pairs $(E ,ϕ\in H^0(End…
Torelli theorem for the moduli space of parabolic Higgs bundles
Tomas L. Gomez, Marina Logares
In this article we extend the proof given by Biswas and Gomez of a Torelli theorem for the moduli space of Higgs bundles with fixed determinant, to the parabolic situation.
Moduli of Parabolic Higgs Bundles and Atiyah Algebroids
Marina Logares, Johan Martens
In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poi…
Moduli spaces of parabolic -Higgs bundles
Oscar Garcia-Prada, Marina Logares, Vicente Muñoz
Using the -norm of the Higgs field as a Morse function, we count the number of connected components of the moduli space of parabolic -Higgs bundles over a Riemann surf…
Betti numbers of parabolic U(2,1)-Higgs bundles moduli spaces
Marina Logares
Let X be a compact Riemann surface together with a finite set of marked points. We use Morse theoretic techniques to compute the Betti numbers of the parabolic U(2,1)-Higgs bundles…