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VOL. 65 | 2015 Dual cones of varieties of minimal rational tangents
Jun-Muk Hwang

Editor(s) Jungkai Alfred Chen, Meng Chen, Yujiro Kawamata, JongHae Keum


The varieties of minimal rational tangents play an important role in the geometry of uniruled projective manifolds. The goal of this paper is to exhibit their role in the symplectic geometry of the cotangent bundles of uniruled projective manifolds. More precisely, let $X$ be a uniruled projective manifold satisfying the assumption that the VMRT at a general point is smooth. We show that the total family of dual cones of the varieties of minimal rational tangents is a coisotropic subvariety in $T^* (X)$. Furthermore, the closure of a general leaf of the null foliation of this coisotropic subvariety is an immersed projective space of dimension $\delta + 1$ where $\delta$ is the dual defect of the variety of minimal rational tangents at a general point. When $\delta = 0$, the symplectic reduction of the coisotropic variety can be realized as a subbundle of the cotangent bundle $T^* (\mathcal{K})$ of the parameter space $\mathcal{K}$ of the rational curves.


Published: 1 January 2015
First available in Project Euclid: 19 October 2018

zbMATH: 1360.14110
MathSciNet: MR3380779

Digital Object Identifier: 10.2969/aspm/06510123

Primary: 14J40

Rights: Copyright © 2015 Mathematical Society of Japan


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