Isotrivial VMRT-structures of complete intersection type

Baohua Fu; Jun-Muk Hwang

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arXiv · 1608.00846

Isotrivial VMRT-structures of complete intersection type

Baohua Fu·Jun-Muk Hwang

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Abstract

The family of varieties of minimal rational tangents on a quasi-homogeneous projective manifold is isotrivial. Conversely, are projective manifolds with isotrivial varieties of minimal rational tangents quasi-homogenous? We will show that this is not true in general, even when the projective manifold has Picard number 1. In fact, an isotrivial family of varieties of minimal rational tangents needs not be locally flat in differential geometric sense. This leads to the question for which projective variety Z, the Z-isotriviality of varieties of minimal rational tangents implies local flatness. Our main result verifies this for many cases of Z among complete intersections.

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Baohua Fu, Jun-Muk Hwang. 2016-08-02. Isotrivial VMRT-structures of complete intersection type. https://arxiv.org/abs/1608.00846

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