# Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018  pp. 693–719.

Lagrangian Subvarieties in the Chow Ring of Some Hyperkähler Varieties

Authors:  Robert Laterveer (1)
Author institution:(1) Institut de Recherche Mathématique Avancée, CNRS – Université de Strasbourg, 7 Rue René Descartes, 67084 Strasbourg CEDEX, FRANCE

Summary:

Let X be a hyperkähler variety, and let ZX be a Lagrangian subvariety. Conjecturally, Z should have trivial intersection with certain parts of the Chow ring of X. We prove this conjecture for certain Hilbert schemes X having a Lagrangian fibration, and ZX a general fibre of the Lagrangian fibration.

2010 Math. Subj. Class. Primary: 14C15, 14C25, 14C30.

Keywords: Algebraic cycles, Chow ring, motives, Bloch–Beilinson filtration, hyperkähler variety, Lagrangian subvariety, constant cycle subvariety, (Hilbert scheme of) K3 surface, Beauville’s splitting property, multiplicative Chow–Künneth decomposition, spread of algebraic cycles.