Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(d) Pairs over Smooth Curves: I
نویسنده
چکیده
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 is given.
منابع مشابه
On the Logarithmic Connections over Curves
We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves. Firstly, we establish a dictionary between logarithmic orbifold connections and parabolic logarithmic connections over the quotient curve. Secondly, we prove that fixed points on the moduli space of connections under the action of finite order line bundles are exactly the push-f...
متن کاملQuantization of a Moduli Space of Parabolic Higgs Bundles
Let MH be a moduli space of stable parabolic Higgs bundles of rank two over a Riemann surface X . It is a smooth variety over C equipped with a holomorphic symplectic form. Fix a projective structure P on X . Using P , we construct a quantization of a certain Zariski open dense subset of the symplectic variety MH .
متن کاملBetti Numbers of the Moduli Space of Rank 3 Parabolic Higgs Bundles
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. In this paper we calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submani...
متن کاملSymplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme
Parabolic triples of the form (E∗, θ, σ) are considered, where (E∗, θ) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and σ is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E∗, θ) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bu...
متن کاملMODULI SPACES OF PARABOLIC U(p, q)-HIGGS BUNDLES
Using the L-norm of the Higgs field as a Morse function, we count the number of connected components of the moduli space of parabolic U(p, q)-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...
متن کامل