Mathematical Research Letters

Volume 24 (2017)

Number 5

Fano $5$-folds with nef tangent bundles

Pages: 1453 – 1475



Akihiro Kanemitsu (Graduate School of Mathematical Sciences, University of Tokyo, Japan)


We prove that Fano $5$-folds with nef tangent bundles are rational homogeneous manifolds.

The author wishes to express his gratitude to Professor Yoichi Miyaoka, his supervisor, for his encouragement, comments and suggestions. He is also grateful to Professor Hiromichi Takagi and Professor Kiwamu Watanabe for their helpful comments and suggestions. The author also wishes to thank Professor Keiji Oguiso and Doctor Charlie Stibitz for helpful comments about Lemma 3.5. The author is a JSPS Research Fellow and he is supported by the Grant-in-Aid for JSPS fellows (JSPS KAKENHI Grant Number 15J07608). This work was supported by the Program for Leading Graduate Schools, MEXT, Japan.

Received 8 November 2015

Accepted 18 July 2016

Published 29 December 2017