Abstract
The space of holomorphic maps from S^{2} to a complex algebraic variety X, i.e. the space of parametrized rational curves on X, arises in several areas of geometry. It is a well known problem to determine an integer n(D) such that the inclusion of this space in the corresponding space of continuous maps induces isomorphisms of homotopy groups up to dimension n(D), where D denotes the homotopy class of the maps. The solution to this problem is known for an important but special class of varieties, the generalized flag manifolds: such an integer may be computed, and n(D) → ∞ as D → ∞. We consider the problem for another class of varieties, namely, toric varieties. For smooth toric varieties and certain singular ones, n(D) may be computed, and n(D) → ∞ as D → ∞. For other singular toric varieties, however, it turns out that n(D) cannot always be made arbitrarily large by a suitable choice of D.
Original language  English 

Pages (fromto)  191196 
Number of pages  6 
Journal  Bulletin of the American Mathematical Society 
Volume  31 
Issue number  2 
DOIs 

Publication status  Published  1994 Oct 
Externally published  Yes 
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics