. A G ] 1 6 O ct 1 99 8 Moduli of bundles on the blown - up plane

O ct 1 99 8 The moduli space M n ( Σ ) of stable fiber bundles over a compact Riemann surface A . Balan Ecole Polytechnique

An introduction to the moduli space of holomorphic fiber bundles M n (Σ) on a compact Riemann surface Σ is presented and a formula for the regularised determinant and an other for the symplectic form at trivial bundle is proposed. Classification AMS 53C07.

O ct 1 99 8 The moduli space M n ( Σ ) of stable fiber bundles over a compact Riemann surface A . Balan Ecole Polytechnique Centre

The moduli space of holomorphic fiber bundles M n (Σ) over a compact Riemann surface Σ is considered. A formula for the regularised determinant and an other for the symplectic form at trivial bundle are proposed.

ar X iv : d g - ga / 9 51 00 06 v 1 2 3 O ct 1 99 5 GROUP SYSTEMS , GROUPOIDS , AND MODULI SPACES OF PARABOLIC BUNDLES

Higgs Bundles and Geometric Structures on Surfaces

Introduction 1 1. Representations of the fundamental group 3 2. Abelian groups and rank one Higgs bundles 5 3. Stable vector bundles and Higgs bundles 6 4. Hyperbolic geometry: G = PSL(2,R) 8 5. Moduli of hyperbolic structures and representations 13 6. Rank two Higgs bundles 19 7. Split R-forms and Hitchin’s Teichmüller component 21 8. Hermitian symmetric spaces: Maximal representations 24 Refe...

X iv : a lg - g eo m / 9 21 00 07 v 1 1 9 O ct 1 99 2 Stable pairs , linear systems and the Verlinde formula

Let X be a smooth projective complex curve of genus g ≥ 2, let Λ→X be a line bundle of degree d > 0, and let (E, φ) be a pair consisting of a vector bundle E →X such that Λ 2 E = Λ and a section φ ∈ H 0 (E) − 0. This paper will study the moduli theory of such pairs. However, it is by no means a routine generalization of the well-known theory of stable bundles. Rather, it will discuss at least t...