On the automorphisms of hyperplane sections of generalized Grassmannians
Résumé
Given a smooth hyperplane section H of a rational homogeneous space G/P with Picard number one, we address the question whether it is always possible to lift an automorphism of H to the Lie group G, or more precisely to Aut(G/P). Using linear spaces and quadrics in H, we show that the answer is positive up to a few well understood exceptions related to Jordan algebras. When G/P is an adjoint variety, we show how to describe Aut(H) completely, extending results obtained by Prokhorov and Zaidenberg when G is the exceptional group G_2.
Domaines
Géométrie algébrique [math.AG]Origine | Fichiers produits par l'(les) auteur(s) |
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