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

M. A. Guest*


研究成果: Comment/debate査読

1 被引用数 (Scopus)


The space of holomorphic maps from S2 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.

ジャーナルBulletin of the American Mathematical Society
出版ステータスPublished - 1994 10月

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学


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