Configuration spaces and the space of rational curves on a toric variety

Author:
M. A. Guest

Journal:
Bull. Amer. Math. Soc. **31** (1994), 191-196

MSC:
Primary 55P99; Secondary 14M25, 55Q99

MathSciNet review:
1260521

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Abstract: The space of holomorphic maps from 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 such that the inclusion of this space in the corresponding space of continuous maps induces isomorphisms of homotopy groups up to dimension , 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 as . We consider the problem for another class of varieties, namely, toric varieties. For smooth toric varieties and certain singular ones, may be computed, and as . For other singular toric varieties, however, it turns out that cannot always be made arbitrarily large by a suitable choice of *D*.

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DOI:
http://dx.doi.org/10.1090/S0273-0979-1994-00515-4

Article copyright:
© Copyright 1994
American Mathematical Society