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Curve classes on irreducible holomorphic symplectic varieties

Department of Mathematics, Alma mater studiorum Università di Bologna, Piazza di Porta san Donato 5, 40126 Bologna, Italy

E-mail Address: [email protected]

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and

John Christian Ottem

Department of Mathematics, University of Oslo, Box 1053, Blindern, 0316 Oslo, Norway

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219199719500780Cited by:5 (Source: Crossref)

Abstract

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of $K 3^{[n]}$ -type and of generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.

Keywords:

AMSC: 14C25, 14J40

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