Simplicity of tangent bundles of smooth horospherical varieties of Picard number one
Abstract
Recently, Kanemitsu has discovered a counterexample to the longstanding conjecture that the tangent bundle of a Fano manifold of Picard number one is (semi)stable. His counterexample is a smooth horospherical variety. There is a weaker conjecture that the tangent bundle of a Fano manifold of Picard number one is simple. We prove that this weaker conjecture is valid for smooth horospherical varieties of Picard number one. Our proof follows from the existence of an irreducible family of unbendable rational curves whose tangent vectors span the tangent spaces of the horospherical variety at general points.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.01512
 Bibcode:
 2021arXiv210701512H
 Keywords:

 Mathematics  Algebraic Geometry;
 14D20;
 14M22