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Fano manifolds and stability of tangent bundles

  • Akihiro Kanemitsu

Abstract

We determine the stability/instability of the tangent bundles of the Fano varieties in a certain class of two orbit varieties, which are classified by Pasquier in 2009. As a consequence, we show that some of these varieties admit unstable tangent bundles, which disproves a conjecture on stability of tangent bundles of Fano manifolds.

Award Identifier / Grant number: 18J00681

Funding statement: The author is a JSPS Research Fellow and supported by the Grant-in-Aid for JSPS fellows (JSPS KAKENHI Grant Number 18J00681).

Acknowledgements

The author wishes to express his gratitude to Professors Gianluca Occhetta and Luis Eduardo Solá Conde for helpful discussions on the geometry of horospherical varieties. He is also grateful to Professors Kento Fujita and Yuji Odaka for helpful comments and discussions on K-stability of Fano manifolds. He also wishes to thank Professor Shigeru Mukai for various discussions, mainly for discussions on the geometry of a Mukai manifold 𝒫 A 1 × G 2 . He is also grateful to the referee for careful reading of the manuscript and for helpful comments and suggestions.

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Received: 2020-07-01
Revised: 2020-10-23
Published Online: 2020-12-15
Published in Print: 2021-05-01

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