Curve classes on irreducible holomorphic symplectic varieties

2018/05/30 by Mongardi, Giovanni, Ottem, John Christian
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.12019

Abstract

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.

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• Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties
• Matroids and the integral Hodge conjecture for abelian varieties
• Curve Classes on Calabi-Yau Complete Intersections in Toric Varieties
• Hodge cycles on some moduli spaces
• Integral Hodge classes on fourfolds fiberd by quadric bundles