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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Geometry of the moduli of parabolic bundles on elliptic curves
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by Néstor Fernández Vargas PDF
Trans. Amer. Math. Soc. 374 (2021), 3025-3052 Request permission


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 $\mathbb {P}^1 \times \mathbb {P}^1$. We also showcase a special curve $\Gamma$ 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 $\mathbb {P}^1$ via a modular map which turns out to be the 2:1 cover ramified in $\Gamma$. 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:
  • 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).
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 3025-3052
  • MSC (2020): Primary 14H60; Secondary 14D20, 14H52, 14Q10
  • DOI:
  • MathSciNet review: 4237941