The connectedness of the moduli space of maps to homogeneous spaces

Abstract

We prove the connectedness of the moduli space of maps (of fixed genus and homology class) to the homogeneous space G/P by degeneration via the maximal torus action. In the genus 0 case, the irreducibility of the moduli of maps is a direct consequence of connectedness. An analysis of a related Bialynicki-Birula stratification of the map space yields a rationality result: the (coarse) moduli space of genus 0 maps to G/P is a rational variety. The rationality argument depends essentially upon rationality results for quotients of SL2 representations proven by Katsylo and Bogomolov.

arXiv comment14 pages, LaTeX2e

Cited by in corpus (19)

• A geometric invariant theory construction of moduli spaces of stable maps
• The Betti numbers of Mbar_{0,n}(r,d)
• Cohomology of moduli spaces
• On the quantum product of Schubert classes
• The Rationality Problem in Invariant Theory
• Tautological classes on the moduli spaces of stable maps to projective spaces
• GIT Constructions of Moduli Spaces of Stable Curves and Maps
• Asymptotic behaviour of rational curves
• Homogeneous Fibrations over Curves
• Rational families of vector bundles on curves, I
• A GIT Construction of Moduli Spaces of Stable Maps in Positive Characteristic
• Triviality and Split of Vector Bundles on Rationally Connected Varieties
• Kontsevich spaces of rational curves on Fano hypersurfaces
• Divisors on the moduli spaces of stable maps to flag varieties and reconstruction
• The Yang-Mills heat flow on the moduli space of framed bundles on a surface
• The irreducibility of the spaces of rational curves on del Pezzo surfaces
• A reconstruction theorem in quantum cohomology and quantum K-theory
• 2-Cycles on Higher Fano Hypersurfaces
• On D. Peterson's comparison formula for Gromov-Witten invariants