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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2025, Volume 329, Pages 90–99
DOI: https://doi.org/10.4213/tm4457 (Mi tm4457) 		 
Algebraic Gromov's Ellipticity of Cubic Hypersurfaces

Sh. I. Kalimana, M. G. Zaidenbergb

a Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA
b Université Grenoble Alpes, CNRS, Institut Fourier, 38000 Grenoble, France
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DOI: https://doi.org/10.4213/tm4457
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.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: April 24, 2024
Revised: December 14, 2024
Accepted: January 30, 2025
Published: 03.09.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2025, Volume 329, Pages 79–87
DOI: https://doi.org/10.1134/S008154382560067X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Sh. I. Kaliman, M. G. Zaidenberg, “Algebraic Gromov's Ellipticity of Cubic Hypersurfaces”, Birational Geometry and Fano Varieties, Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday, Trudy Mat. Inst. Steklova, 329, Steklov Math. Inst., Moscow, 2025, 90–99; Proc. Steklov Inst. Math., 329 (2025), 79–87
Citation in format AMSBIB
\Bibitem{KalZai25}
\by Sh.~I.~Kaliman, M.~G.~Zaidenberg
\paper Algebraic Gromov's Ellipticity of Cubic Hypersurfaces
\inbook Birational Geometry and Fano Varieties
\bookinfo Collected papers. Dedicated to Yuri Gennadievich Prokhorov on the occasion of his 60th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2025
\vol 329
\pages 90--99
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4457}
\crossref{https://doi.org/10.4213/tm4457}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2025
\vol 329
\pages 79--87
\crossref{https://doi.org/10.1134/S008154382560067X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105017145182}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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