Stability of the tangent bundle of G/P in positive characteristics

Indranil Biswas (1) , Pierre-Emmanuel Chaput (2) , Christophe Mourougane (3)

1 TIFR - Tata Institute for Fundamental Research
2 IECL - Institut Élie Cartan de Lorraine
3 IRMAR - Institut de Recherche Mathématique de Rennes

Let $G$ be an almost simple simply-connected affine algebraic group over an algebraically closed field $k$ of characteristic $p > 0$. If $G$ has type $B_n$, $C_n$ or $F_4$, we assume that $p > 2$, and if $G$ has type $G_2$, we assume that $p > 3$. Let $P \subset G$ be a parabolic subgroup. We prove that the tangent bundle of $G/P$ is Frobenius stable with respect to any polarization on $G/P$.

Mots clés: tangent bundle; stability; Frobenius; Rational homogeneous space

Domaines: Géométrie algébrique [math.AG]

Indranil Biswas, Pierre-Emmanuel Chaput, Christophe Mourougane. Stability of the tangent bundle of G/P in positive characteristics. Algebras and Representation Theory, 2019, 22 (1), pp.239-247. ⟨10.1007/s10468-018-9764-x⟩. ⟨hal-01176194⟩