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- Title
Minimal Rational Curves on Complete Toric Manifolds and Applications.
- Authors
Chen, Yifei; Fu, Baohua; Hwang, Jun-Muk
- Abstract
We show that minimal rational components on a complete toric manifold X correspond bijectively to some special primitive collections in the fan defining X, and the associated varieties of minimal rational tangents are linear subspaces. Two applications are given: the first is a classification of n-dimensional toric Fano manifolds with a minimal rational component of degree n, and the second shows that any complete toric manifold satisfying certain combinatorial conditions on the fan has the target rigidity property.
- Publication
Proceedings of the Edinburgh Mathematical Society, 2014, Vol 57, Issue 1, p111
- ISSN
0013-0915
- Publication type
Article
- DOI
10.1017/S001309151300093X