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.
Funding source: Japan Society for the Promotion of Science
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
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