Papers › Geometry of the moduli of parabolic bundles on elliptic curves
Geometry of the moduli of parabolic bundles on elliptic curves
Néstor Fernández Vargas
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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 ℙ¹ ×ℙ¹. 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 ℙ¹ 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.
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