804 research outputs found
On Higgs Bundles on Nodal Curves
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, we survey on the relation between
representations of the fundamental group of a nodal curve and the moduli spaces
of generalised parabolic bundles and generalised parabolic -twisted Hitchin
pairs on its normalisation as well as on an analogue of the Hitchin map for
generalised parabolic -twisted Hitchin pairs
Moduli spaces of parabolic -Higgs bundles
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 surface with a finite number of marked points, under
certain genericity conditions on the parabolic structure. This space is
homeomorphic to the moduli space of representations of the fundamental group of
the punctured surface in , with fixed compact holonomy classes around
the marked points. We apply our results to the study of representations of the
fundamental group of elliptic surfaces of general type.Comment: 46 pages, no figures. Corrected typos, added remarks. To appear in
"Quarterly Journal of Mathematics
Hodge polynomials of the SL(2, C)-character variety of an elliptic curve with two marked points
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 representations around the marked points to be diagonal and of modulus one, the character variety is diffeomorphic to the moduli space of strongly parabolic Higgs bundles, whose Betti numbers are known. In that case we can recover some of the Hodge numbers of the character variety. We extend this result to the moduli space of doubly periodic instantons
On character varieties of singular manifolds
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 varieties over manifolds with conic singularities, which
we will call nodefolds. This construction is valid for any algebraic group ,
in any dimension and also in the parabolic setting. In particular, this TQFT
allow us to compute the virtual classes of representation varieties over
complex singular planar curves. In addition, in the case , the virtual class of the associated character variety over
a nodal closed orientable surface is computed both in the non-parabolic and in
the parabolic scenarios.Comment: 30 pages, 4 figure
Agua, salud y análisis costo/beneficio social
In this paper, it is shown the relationship between coverage in water and sanitation, and hydric disease’s incidence. There are synthesized the situations of the more affected regions and there are presented the Millennium Development Goals on the subject. Briefly, there are summarized the social cost/benefit analysis applicable to public projects, and it is studied the particular case of its application to the Millennium Development Goals in water and sanitation
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