Configuration spaces and the space of rational curves on a toric variety
| dc.creator | Guest, Martin A. | |
| dc.date | 1994-10-01 | |
| dc.date.accessioned | 2026-07-07T09:15:11Z | |
| dc.date.available | 2026-07-07T09:15:11Z | |
| dc.description | 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 $n(D)\to\infty$ as $D\to\infty$. 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 $n(D)\to\infty$ as $D\to\infty$. For other singular toric varieties, however, it turns out that $n(D)$ cannot always be made arbitrarily large by a suitable choice of $D$. | |
| dc.description | 6 pages | |
| dc.identifier | https://arxiv.org/abs/math/9410219 | |
| dc.identifier | http://arxiv.org/abs/math/9410219 | |
| dc.identifier | Bull. Amer. Math. Soc. (N.S.) 31 (1994) 191-196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152935 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Configuration spaces and the space of rational curves on a toric variety | |
| dc.type | text |