Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type

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

It is known that the cotangent bundle ΩY of an irreducible Hermitian symmetric space Y of compact type is stable. Except for a few obvious exceptions, we show that if X ⊂ Y is a complete intersection such that Pic(Y) → Pic(X) is surjective, then the restriction Ω Y |X is stable. We then address some cases where the Picard group increases by restriction.

Mots clés: Lefschetz theorem; stability of vector bundles; hermitian symmetric spaces; homogeneous spaces

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Indranil Biswas, Pierre-Emmanuel Chaput, Christophe Mourougane. Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type. Publications of the Research Institute for Mathematical Sciences, 2019, 55 (2), pp.283-318. ⟨10.4171/PRIMS/55-2-3⟩. ⟨hal-01138190⟩