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Pré-Publication, Document De Travail Année : 2023

Gromov ellipticity of cones over projective manifolds

M Zaidenberg

Résumé

We find classes of projective manifolds that are elliptic in the sense of Gromov and such that the affine cones over these manifolds also are elliptic off their vertices. For example, the latter holds for any generalized flag manifold of dimension n ≥ 3 successively blown up in a finite set of points and infinitesimally near points. This also holds for any smooth projective rational surface. For the affine cones, the Gromov ellipticity is a much weaker property than the flexibility. Nonetheless, it still implies the infinite transitivity of the action of the endomorphism monoid on these cones.
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Dates et versions

hal-04012441 , version 1 (02-03-2023)
hal-04012441 , version 2 (08-03-2023)

Identifiants

  • HAL Id : hal-04012441 , version 2

Citer

Shulim Kaliman, M Zaidenberg. Gromov ellipticity of cones over projective manifolds. 2023. ⟨hal-04012441v2⟩

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