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Algebraic Gromov's ellipticity of cubic hypersurfaces

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arxiv 2402.04462 v4 pith:NCLQQPE3 submitted 2024-02-06 math.AG

Shulim Kaliman , Mikhail Zaidenberg This is my paper · ORCID
classification math.AG
keywords ellipticgromovcubicsenseaffinealgebraicalgebraicallycone
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We show that every smooth cubic hypersurface X in P^{n+1}, n> 1 is algebraically elliptic in Gromov's sense. This gives the first examples of non-rational projective manifolds elliptic in Gromov's sense. We also deduce that the punctured affine cone over X is elliptic.

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  1. Retract rational varieties are uniformly retract rational

    math.AG 2024-11 conditional novelty 7.0 of 10

    Nonsingular retract rational varieties are uniformly retract rational, implying rational projective complex varieties are algebraically elliptic.

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