Compactification of moduli of Higgs bundles
نویسنده
چکیده
In this paper we consider a canonical compactification of M, the moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface Σ, producing a projective variety M̄ = M∪Z. We give a detailed study of the spaces M̄, Z and M. In doing so we reprove some assertions of Laumon and Thaddeus on the nilpotent cone.
منابع مشابه
On the Morgan-shalen Compactification of the Sl(2,c) Character Varieties of Surface Groups
A gauge theoretic description of the Morgan-Shalen compactification of the SL(2, C) character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space of Higgs bundles via the Hitchin map.
متن کاملGeometry of Moduli Spaces of Higgs Bundles
We construct a Petersson-Weil type Kähler form on the moduli spaces of Higgs bundles over a compact Kähler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature of a certain determinant line bundle, equipped with a Quillen metric, on the moduli space of Higgs bundles over a projective manifold. The curvature of the Peters...
متن کاملThe Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves
We construct the Hilbert compactification of the universal moduli space of semistable vector bundles over smooth curves. The Hilbert compactification is the GIT quotient of some open part of an appropriate Hilbert scheme of curves in a Graßmannian. It has all the properties asked for by Teixidor.
متن کاملModuli Spaces of Parabolic Higgs Bundles and Parabolic K(d) Pairs over Smooth Curves: I
This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D) pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a noncompact, connected, simply connected manifold, and a computation of its Poincaré polynomial ...
متن کاملParabolic Bundles on Algebraic Surfaces I- the Donaldson–uhlenbeck Compactification
The aim of this paper is to construct the parabolic version of the Donaldson–Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non–emptiness of the moduli space of parabolic stable bundles of rank 2 and also prove the existence of components with smooth po...
متن کامل