1. Geometry of the moduli of parabolic bundles on elliptic curves.
- Author
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Vargas, Néstor Fernández
- Subjects
- *
ELLIPTIC curves , *VECTOR bundles , *GEOMETRY , *AUTOMORPHISMS , *HYPERELLIPTIC integrals - Abstract
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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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