Asian Journal of Mathematics

Volume 22 (2018)

Number 2

Special issue in honor of Ngaiming Mok (1 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

Isotrivial VMRT-structures of complete intersection type

Pages: 333 – 354

DOI: http://dx.doi.org/10.4310/AJM.2018.v22.n2.a10

Authors

Baohua Fu (Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China)

Jun-Muk Hwang (Korea Institute for Advanced Study, Seoul, South Korea)

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.

Keywords

equivalence problem, minimal rational curve, complete intersection

2010 Mathematics Subject Classification

14M10, 53B99, 58A15

Full Text (PDF format)

Baohua Fu is supported by National Natural Science Foundation of China (11621061 and 11688101).

Jun-Muk Hwang is supported by National Researcher Program 2010-0020413 of NRF.

Received 25 July 2016

Accepted 27 June 2017

Published 15 June 2018