• Corpus ID: 238253363

On the automorphisms of hyperplane sections of generalized Grassmannians

  title={On the automorphisms of hyperplane sections of generalized Grassmannians},
  author={Vladimiro Benedetti and Laurent Manivel},
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… 

Tables from this paper


The Automorphism Group of Linear Sections of the Grassmannians G(1,N)
The Grassmannians of lines in projective N-space, G(1,N), are embedded by way of the Pl"ucker embedding in the projective space P(\bigwedge^2 C^{N+1}). Let H^l be a general l-codimensional linear
Quivers and the cohomology of homogeneous vector bundles
We describe the cohomology groups of a homogeneous vector bundle E on any Hermitian symmetric variety X = G/P of ADE-type as the cohomology of a complex explicitly described. The main tool is the
Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the
Fano contact manifolds and nilpotent orbits
Abstract. A contact structure on a complex manifold M is a corank 1 subbundle F of TM such that the bilinear form on F with values in the quotient line bundle L = TM/F deduced from the Lie bracket of
Odd symplectic flag manifolds
We define the odd symplectic Grassmannians and flag manifolds, which are smooth projective varieties equipped with an action of the odd symplectic group, analogous to the usual symplectic
On Fano complete intersections in rational homogeneous varieties
Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $$X = \cap _{i=1}^r D_i \subset G/P$$ X = ∩ i = 1 r D i ⊂ G / P is a
Fano-Mukai fourfolds of genus 10 as compactifications of ℂ^4
It is known that the moduli space of smooth Fano-Mukai fourfolds V18 of genus 10 has dimension one. We show that any such fourfold is a completion of C in two different ways. Up to isomorphism, there
Orbit decomposition of Jordan matrix algebras of order three under the automorphism groups
The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the