Parabolic bundles and representations¶of the fundamental group

Parabolic Raynaud Bundles

Let X be an irreducible smooth projective curve defined over complex numbers, S = {p1, p2, . . . , pn} ⊂ X a finite set of closed points and N ≥ 2 a fixed integer. For any pair (r, d) ∈ N × 1 N Z, there exists a parabolic vector bundle Rr,d,∗ on X , with parabolic structure over S and all parabolic weights in 1 N Z, that has the following property: Take any parabolic vector bundle E∗ of rank r ...

The Verlinde Formula for Parabolic Bundles

Let Σ be a compact Riemann surface of genus g, and G ̄SU(n). The central element c ̄ diag(e#id/n,... , e#id/n) for d coprime to n is introduced. The Verlinde formula is proved for the Riemann–Roch number of a line bundle over the moduli space g," (c,Λ) of representations of the fundamental group of a Riemann surface of genus g with one boundary component, for which the loop around the boundary is...

Semistable Bundles on Curves and Reducible Representations of the Fundamental Group Hélène Esnault and Claus Hertling

A.A. Bolibruch [3] and V.P. Kostov [8] showed independently that if ρ : π1(P 1 \ Σ) → GL(n,C) is an irreducible representation of the fundamental group, then there is an algebraic bundle E together with an algebraic connection ∇ : E → Ω(log Σ)⊗ E with underlying local system ρ, with the property that E ∼= ⊕1O is algebraically trivial. Equivalently, E can be taken to be the twist L ⊗ (⊕1O) of a ...

p-adic vector bundles on curves and abelian varieties and representations of the fundamental group

Representations of Orbifold Groups and Parabolic Bundles