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Geometry of the moduli of parabolic bundles on elliptic curves.
- Source :
-
Transactions of the American Mathematical Society . May2021, Vol. 374 Issue 5, p3025-3052. 28p. - Publication Year :
- 2021
-
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]
- Subjects :
- *ELLIPTIC curves
*VECTOR bundles
*GEOMETRY
*AUTOMORPHISMS
*HYPERELLIPTIC integrals
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 149592939
- Full Text :
- https://doi.org/10.1090/tran/7330