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Rationality, universal
generation and the integral Hodge conjecture
Mingmin Shen |
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Geometry & Topology 23 (2019) 2861–2898
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Abstract |
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We use the universal generation of algebraic cycles to relate (stable) rationality to the integral Hodge conjecture. We show that the Chow group of –cycles on a cubic hypersurface is universally generated by lines. Applications are mainly in cubic hypersurfaces of low dimensions. For example, we show that if a generic cubic fourfold is stably rational then the Beauville–Bogomolov form on its variety of lines, viewed as an integral Hodge class on the self product of its variety of lines, is algebraic. In dimensions and , we relate stable rationality with the geometry of the associated intermediate Jacobian. |
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Keywords
algebraic cycles, Hodge conjecture, cubic threefold, cubic
fourfold
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Mathematical Subject Classification 2010
Primary: 14C25, 14C30, 14E08
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References |
Publication
Received: 12 December 2016
Revised: 24 January 2019
Accepted: 26 February 2019
Published: 1 December 2019
Proposed: Dan Abramovich
Seconded: Richard P Thomas, Jim Bryan
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Authors |
| Mingmin Shen | |
| KdV Institute for Mathematics University of Amsterdam Amsterdam Netherlands |
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