On spaces of maps from Riemann surfaces to Grassmannians and applications to the cohomology of moduli of vector bundles

DOI10.1007/BF02384399zbMath0625.14026MaRDI QIDQ579360

Frances C. Kirwan

Publication date: 1986

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

holomorphic mapsRiemann surfaceGrassmann manifoldquotientscohomology of the moduli spaces of holomorphic bundles on curves

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Geometric invariant theory (14L24) Grassmannians, Schubert varieties, flag manifolds (14M15) Families, moduli of curves (algebraic) (14H10) Algebraic moduli problems, moduli of vector bundles (14D20)

Related Items

HOMOTOPY GROUPS OF MODULI SPACES OF STABLE QUIVER REPRESENTATIONS, On the Abel-Jacobi map for divisors of higher rank on a curve, The Kuranishi map for vector bundles on certain products of curves, The stringy E-function of the moduli space of rank 2 bundles over a Riemann surface of genus 3, Rational intersection cohomology of quotient varieties, The topology of the space of rational maps into generalized flag manifolds, The cohomology of holomorphic self maps of the Riemann sphere, Holomorphic curves in loop groups, Three applications of instanton numbers, Configuration spaces and the space of rational curves on a toric variety, Algebraic independence of generalized MMM-classes, On the geometry of moduli spaces of anti-self-dual connections, On the topology of spaces of holomorphic maps, Spaces of non-degenerate maps between complex projective spaces, The Atiyah-Jones conjecture for rational surfaces, The topology of rational functions and divisors of surfaces, Compactified spaces of holomorphic curves in complex Grassmann manifolds, Lectures on \(2\)D Yang-Mills theory, equivariant cohomology and topological field theories, Desingularizations of the moduli space of rank 2 bundles over a curve, Problems in arithmetic topology, The Cohomology Rings of Moduli Spaces of Bundles over Riemann Surfaces, STABILITY THEOREMS FOR SPACES OF RATIONAL CURVES, STABILITY THEOREMS FOR SPACES OF RATIONAL CURVES, Yang-Mills connections on orientable and nonorientable surfaces, Momentum maps and reduction in algebraic geometry, Yang–Mills theory and jumping curves, An algebraic compactification for spaces of holomorphic curves in complex Grassmann manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Module des fibrés stables sur les courbes algébriques. Notes de l'Ecole Normale Supérieure (Paris), Printemps, 1983
• The topology of spaces of rational functions
• Configuration spaces of positive and negative particles
• Homology fibrations and the 'group-completion' theorem
• On the cohomology groups of moduli spaces of vector bundles on curves
• Lectures on introduction to moduli problems and orbit spaces
• Space of unitary vector bundles on a compact Riemann surface
• Moduli of vector bundles on a compact Riemann surface
• Topology of the Space of Absolute Minima of the Energy Functional
• ON THE ZEEMAN COMPARISON THEOREM FOR THE HOMOLOGY OF QUASI-NILPOTENT FIBRATIONS
• The Yang-Mills equations over Riemann surfaces
• Singular Points of Complex Hypersurfaces. (AM-61)