Advances in Theoretical and Mathematical Physics

Volume 16 (2012)

Number 2

Vortex equation and reflexive sheaves

Pages: 713 – 723

DOI: http://dx.doi.org/10.4310/ATMP.2012.v16.n2.a8

Authors

Indranil Biswas (School of Mathematics, Tata Institute of Fundamental Research, Bombay, India)

Matthias Stemmler (School of Mathematics, Tata Institute of Fundamental Research, Bombay, India)

Abstract

It is known that given a stable holomorphic pair $(E, φ) $, where $E$ is a holomorphic vector bundle on a compact Kähler manifold $X$ and $φ$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. We generalize this to pairs $(E, φ)$, where $E$ is a reflexive sheaf on $X$.

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