English

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.

Keywords

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

R2 v1 2026-07-22T18:02:19.104Z