Stability Theorems for Spaces of Rational Curves

1999/03/16 by C. P. Boyer, J. C. Hurtubise, R. J. Milgram
Mathematics · #math.AG #math.AT

paper · pdf

published as Int. Journ. of Math. 12(2) (2001), 223-262 · 37 pages, Revised Version

arxiv created 1999/03/16 · arxiv updated 2009/11/30

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.

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