The vortex equation on affine manifolds

Indranil Biswas, John Loftin, Matthias Stemmler

Research output: Contribution to journalArticle

Abstract

Let M be a compact connected special affine manifold equipped with an affine Gauduchon metric. We show that a pair (E, φ), consisting of a flat vector bundle E over M and a flat nonzero section φ 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.

Original languageEnglish (US)
Pages (from-to)3925-3941
Number of pages17
JournalTransactions of the American Mathematical Society
Volume366
Issue number7
DOIs
StatePublished - Jan 1 2014

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Affine manifold
  • Dimensional reduction
  • Stability
  • Vortex equation

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