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1 April 2019 Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
Francesco Russo, Giovanni Staglianò
Duke Math. J. 168(5): 849-865 (1 April 2019). DOI: 10.1215/00127094-2018-0053

Abstract

The works of Hassett and Kuznetsov identify countably many divisors Cd in the open subset of P55=P(H0(OP5(3))) parameterizing all cubic fourfolds and conjecture that the cubics corresponding to these divisors are precisely the rational ones. Rationality has been known classically for the first family C14. We use congruences of 5-secant conics to prove rationality for the first three of the families Cd, corresponding to d=14,26,38 in Hassett’s notation.

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Francesco Russo. Giovanni Staglianò. "Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds." Duke Math. J. 168 (5) 849 - 865, 1 April 2019. https://doi.org/10.1215/00127094-2018-0053

Information

Received: 29 October 2017; Revised: 11 July 2018; Published: 1 April 2019
First available in Project Euclid: 5 March 2019

zbMATH: 07055194
MathSciNet: MR3934590
Digital Object Identifier: 10.1215/00127094-2018-0053

Subjects:
Primary: 14E08
Secondary: 14M07 , 14M20 , 14N05 , 14Q10

Keywords: cubic fourfold , Kuznetsov conjecture , rationality of cubic hypersurfaces

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 5 • 1 April 2019
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