Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians

  title={Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians},
  author={Aaron Bertram and Georgios K Daskalopoulos and Richard A. Wentworth},
Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the Grothendieck Quot Scheme. The latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by Bradlow. This gives an effective way of computing certain… CONTINUE READING
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