Fano manifolds and stability of tangent bundles

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.

18 pages

References in corpus (1)

• Cohomological characterizations of projective spaces and hyperquadrics

Cited by in corpus (1)

• The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds