Gromov Invariants for Holomorphic Maps from Riemann Surfaces to Grassmannians

Abstract

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 scheme and is dominated by the algebraic compactification arising as a 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 intersection numbers (known as Gromov invariants) on the space of holomorphic maps into Grassmannians. We carry out these computations in the case where the Riemann surface has genus one.

52 pages, Plain TeX

References in corpus (1)

• Birational Equivalences of Vortex Moduli

Cited by in corpus (6)

• The Master Space of N=1 Gauge Theories
• J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions
• On Quantum Cohomology Rings of Fano Manifolds and a Formula of Vafa and Intriligator
• Birational Equivalences of Vortex Moduli
• Rank-level duality of conformal blocks of GL_n and SL_n
• Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian