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Minimal Rational Curves on Complete Toric Manifolds and Applications

Published online by Cambridge University Press:  17 December 2013

Yifei Chen ,
Baohua Fu  and
Jun-Muk Hwang
Yifei Chen
Affiliation:
Institute of Mathematics, AMSS, 55 Zhongguancun East Road, Beijing 100190, People's Republic of China (yifeichen@amss.ac.cn; bhfu@math.ac.cn)
Baohua Fu
Affiliation:
Institute of Mathematics, AMSS, 55 Zhongguancun East Road, Beijing 100190, People's Republic of China (yifeichen@amss.ac.cn; bhfu@math.ac.cn)
Jun-Muk Hwang
Affiliation:
Korea Institute for Advanced Study, Hoegiro 87, Seoul 130-722, Republic of Korea (jmhwang@kias.re.kr)
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Abstract

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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.

Keywords

toric varietiesrational curvesvarieties of minimal rational tangentsPrimary 14M25
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 1 , February 2014 , pp. 111 - 123
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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