## Beauville's splitting principle for Chow rings of projective hyperkaehler manifolds

Lie Fu

Member, School of Mathematics

November 4, 2014

Being the natural generalization of K3 surfaces, hyperkaehler varieties, also known as irreducible holomorphic symplectic varieties, are one of the building blocks of smooth projective varieties with trivial canonical bundle. One of the guiding conjectures in the study of algebraic cycles of such varieties is Beauville's splitting principle. Concerning the weak form of the splitting principle, I want to report some progress on the closely related Beauville-Voisin conjecture.