This article is cited in 2 papers

Algebraic Gromov's Ellipticity of Cubic Hypersurfaces

Sh. I. Kaliman^a, M. G. Zaidenberg<sup>b

a</sup> Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA
^b Université Grenoble Alpes, CNRS, Institut Fourier, 38000 Grenoble, France

Abstract: We show that every smooth cubic hypersurface $X$ in $\mathbb P^{n+1}$, $n\ge 2$, is algebraically elliptic in Gromov's sense. This gives the first examples of nonrational projective manifolds elliptic in Gromov's sense. We also deduce that the punctured affine cone over $X$ is elliptic.

Keywords: spray, Gromov's ellipticity, unirationality, stable rationality, cubic threefold, cubic hypersurface, affine cone.

Received: April 24, 2024
Revised: December 14, 2024
Accepted: January 30, 2025

DOI: 10.4213/tm4457

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 329, 79–87

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