Geometry of the moduli of parabolic bundles on elliptic curves
Author:
Néstor Fernández Vargas
Journal:
Trans. Amer. Math. Soc. 374 (2021), 3025-3052
MSC (2020):
Primary 14H60; Secondary 14D20, 14H52, 14Q10
DOI:
https://doi.org/10.1090/tran/7330
Published electronically:
February 23, 2021
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Abstract | References | Similar Articles | Additional Information
Abstract: The goal of this paper is the study of simple rank 2 parabolic vector bundles over a -punctured elliptic curve
. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to
. We also showcase a special curve
isomorphic to
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
via a modular map which turns out to be the 2:1 cover ramified in
. 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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Additional Information
Néstor Fernández Vargas
Affiliation:
IRMAR Université Rennes 1 F-35000 Rennes France
Email:
nestor.fernandez-vargas@univ-rennes1.fr
DOI:
https://doi.org/10.1090/tran/7330
Keywords:
Parabolic vector bundle,
parabolic structure,
elliptic curve,
moduli space,
del Pezzo surface
Received by editor(s):
November 23, 2016
Received by editor(s) in revised form:
June 21, 2017
Published electronically:
February 23, 2021
Additional Notes:
The author gratefully acknowledges support by the Centre Henri Lebesgue (ANR-11-LABX-0020-01).
Article copyright:
© Copyright 2021
American Mathematical Society