Stability Theorems for Spaces of Rational Curves
Algebraic Geometry
2007-05-23 v1 Algebraic Topology
Abstract
Let X be a smooth algebraic variety on which a solvable Lie group acts freely on a dense open orbit. Such varieties include generalized flag varieties, toric varieties, Bott-Samelson varieties, and many spherical varieties, as well as equivariant blow-ups of these. We prove that the space of based holomorphic maps from the Riemann sphere to X approximates in an appropriate sense, both in homology and in homotopy the space of all continuous based maps from the 2-sphere to X, that is the 2-fold loop space of X.
Cite
@article{arxiv.math/9903099,
title = {Stability Theorems for Spaces of Rational Curves},
author = {C. P. Boyer and J. C. Hurtubise and R. J. Milgram},
journal= {arXiv preprint arXiv:math/9903099},
year = {2007}
}
Comments
37 pages, Revised Version