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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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The vortex equation on affine manifolds
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by Indranil Biswas, John Loftin and Matthias Stemmler PDF
Trans. Amer. Math. Soc. 366 (2014), 3925-3941 Request permission

Abstract:

Let $M$ be a compact connected special affine manifold equipped with an affine Gauduchon metric. We show that a pair $(E, \phi )$, consisting of a flat vector bundle $E$ over $M$ and a flat nonzero section $\phi$ of $E$, admits a solution to the vortex equation if and only if it is polystable. To prove this, we adapt the dimensional reduction techniques for holomorphic pairs on Kähler manifolds to the situation of flat pairs on affine manifolds.
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Additional Information
  • Indranil Biswas
  • Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
  • MR Author ID: 340073
  • Email: indranil@math.tifr.res.in
  • John Loftin
  • Affiliation: Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102
  • Email: loftin@rutgers.edu
  • Matthias Stemmler
  • Affiliation: Fachbereich Mathematik und Informatik, Philipps–Universität Marburg, Hans–Meerwein–Straße, Lahnberge, 35032 Marburg, Germany
  • Email: stemmler@mathematik.uni-marburg.de
  • Received by editor(s): November 19, 2012
  • Received by editor(s) in revised form: January 26, 2013
  • Published electronically: March 20, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 3925-3941
  • MSC (2010): Primary 53C07, 57N16
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06152-7
  • MathSciNet review: 3192624