51 citations · 407 across the 34 of their papers we have counts for
36 papers
Stringy invariants for abelian character varieties
Carlos Florentino, Ángel González-Prieto, Alfonso Zamora
We compute all stringy invariants, encoding orbifold cohomology numbers, of (the normalization of) the identity component of -character varieties of free abelian groups and of m…
Character Varieties of Generalized Torus Knot Groups
Carlos Florentino, Sean Lawton
Given , let be a group presentable as $$\left\langle γ_{1},\ldots,γ_{r}\:|\:γ_{1}^{n_{1}}=γ_{2}^{n_{2}}=\cdots=γ_{r…
Topology of the moduli spaces of Higgs bundles over abelian varieties
Indranil Biswas, Carlos Florentino, Azizeh Nozad
Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over . We determine the Poincaré polynomials and also the mixed Hodge polynomial…
Mixed Hodge structures on character varieties of nilpotent groups
Carlos Florentino, Sean Lawton, Jaime Silva
Let R be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected reductive complex affine algebraic gro…
Plethystic exponential calculus and characteristic polynomials of permutations
Carlos A. A. Florentino
We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae…
Flawed groups and the topology of character varieties
Carlos Florentino, Sean Lawton
A finitely presented group F is called flawed if Hom(F,G)//G deformation retracts onto its subspace Hom(F,K)/K for reductive affine algebraic groups G and maximal compact subgroups…
On Hodge polynomials of Singular Character Varieties
Carlos Florentino, Azizeh Nozad, Jaime Silva +1
Let be the -character variety of , where is a complex reductive group and a finitely presented group. We introduce new techni…
Serre polynomials of - and -character varieties of free groups
Carlos Florentino, Azizeh Nozad, Alfonso Zamora
Let be a complex reductive group and denote the -character variety of the free group of rank . Using geometric methods, we prove that $E(\mathcal{X}_{r…
Generating series for the -polynomials of -character varieties
Carlos Florentino, Azizeh Nozad, Alfonso Zamora
With G=GL(n,C), let be the G-character variety of a given finitely presented group , and let be the locus of irred…
Daniel Augusto da Silva, Poet of Mathematics
Carlos A. A. Florentino
Daniel da Silva was a remarkable Scientist and Mathematician of the mid 19th century. Working in Portugal, isolated from the main scientific centres of the time, his investigations…
Hodge-Deligne polynomials of character varieties of abelian groups
Carlos A. Florentino, Jaime A. M. Silva
Let F be a finite group and X be a complex quasi-projective F-variety. For r in N, we consider the mixed Hodge-Deligne polynomials of quotients X^r/F, where F acts diagonally, and…
Principal Schottky Bundles over Riemann surfaces
A. C. Casimiro, S. Ferreira, C. Florentino
We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to…
Higgs bundles and representation spaces associated to morphisms
Indranil Biswas, Carlos Florentino
Let be a connected reductive affine algebraic group defined over the complex numbers, and be a maximal compact subgroup. Let be irreducible smooth complex…
Homotopy type of free group character varieties
Ana Casimiro, Carlos Florentino, Sean Lawton +1
Let G be a real reductive algebraic group with maximal compact subgroup K, and let F be a rank r free group. Here, we summarize the construction of a natural strong deformation ret…
Homotopy Groups of Free Group Character Varieties
Carlos Florentino, Sean Lawton, Daniel Ramras
Let G be a connected, complex reductive Lie group with maximal compact subgroup K, and let X denote the moduli space of G- or K-valued representations of a rank r free group. In th…
Character varieties of virtually nilpotent Kähler groups and G-Higgs bundles
Indranil Biswas, Carlos Florentino
Let G be a connected complex reductive affine algebraic group, and let K be a maximal compact subgroup. Let X be a compact connected Kähler manifold whose fundamental group Gamma i…
Topology of Moduli Spaces of Free Group Representations in Real Reductive Groups
Ana Casimiro, Carlos Florentino, Sean Lawton +1
Let be a real reductive algebraic group with maximal compact subgroup , and let be a rank free group. We show that the space of closed orbits in $\mathrm{Hom}(F_r,…
Symplectic form on hyperpolygon spaces
Indranil Biswas, Carlos Florentino, Leonor Godinho +1
In [GM], a family of parabolic Higgs bundles on has been constructed and identified with a moduli space of hyperpolygons. Our aim here is to give a canonical alternative con…
Commuting elements in reductive groups and Higgs bundles on abelian varieties
Indranil Biswas, Carlos Florentino
Let G be a connected real reductive algebraic group, and let K be a maximal compact subgroup of G. We prove that the conjugation orbit space Hom(Z^{2d},K)/K is a strong deformation…
Topology of character varieties of Abelian groups
C. Florentino, S. Lawton
Let G be a complex reductive algebraic group (not necessarily connected), let K be a maximal compact subgroup, and let A be a finitely generated Abelian group. We prove that the co…
Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1
Indranil Biswas, Carlos Florentino, Leonor Godinho +1
Consider the moduli space of parabolic Higgs bundles (E,Φ) of rank two on CP^1 such that the underlying holomorphic vector bundle for the parabolic vector bundle E is trivial. It i…
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…
Quantization of some moduli spaces of parabolic vector bundles on CP^1
Indranil Biswas, Carlos Florentino, José Mourão +1
We address quantization of the natural symplectic structure on a moduli space of parabolic vector bundles of parabolic degree zero over with four parabolic points a…
Stability of Affine G-varieties and Irreducibility in Reductive Groups
Ana Casimiro, Carlos Florentino
Let be a reductive affine algebraic group, and let be an affine algebraic -variety. We establish a (poly)stability criterion for points in terms of intrinsicall…