Birational Equivalences of Vortex Moduli

1993/04/06 by Steven B. Bradlow, S. Bradlow, Bradlow, S. +6 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9304001

40 pages in Plain TeX (same as the original, but with TeXnical errors removed)

arxiv created 1993/04/08 · arxiv updated 2009/11/30

Abstract

We construct a finite dimensional Kaehler manifold with a holomorphic, symplectic circle action whose symplectic reduced spaces may be identified with the tau-vortex moduli spaces (or tau-stable pairs). The Morse theory of the circle action induces natural birational maps between the reduced spaces for different values of tau which in the case of rank two bundles can be canonically resolved in a sequence of blow-ups and blow-downs.

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• Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians

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