Geometry of the moduli of parabolic bundles on elliptic curves
Résumé
The goal of this paper is the study of simple rank 2 parabolic vector bundles over a 2-punctured elliptic curve C. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to ℙ^1×ℙ^1. We also showcase a special curve Γ isomorphic to C embedded in this space, and this way we prove a Torelli theorem.This moduli space is related to the moduli space of semistable parabolic bundles over ℙ^1 via a modular map which turns out to be the 2:1 cover ramified in Γ. We recover the geometry of del Pezzo surfaces of degree 4 and we reconstruct all their automorphisms via elementary transformations of parabolic vector bundles.