Chow rings and modified diagonals

Topology of Algebraic Varieties
Topic:Chow rings and modified diagonals
Speaker:Kieran O'Grady
Affiliation:Sapienza - Università di Roma; Member, School of Mathematics
Date:Tuesday, October 7
Time/Room:2:00pm - 3:00pm/S-101
Video Link:http://video.ias.edu/tav/2014/1007-KieranOGrady

Beauville and Voisin proved that decomposable cycles (intersections of divisors) on a projective K3 surface span a 1-dimensional subspace of the (infinite-dimensional) group of 0-cycles modulo rational equivalence. I will address the following question: what is the rank of the group of decomposable 0-cycles of a smooth projective variety? Beauville and Voisin also proved a refinement of the result mentioned above, namely a decomposition (modulo rational equivalence) of the small diagonal in the cube of a K3. Motivated by this result we will discuss modified diagonals and their relation with conjectures of Beauville and Voisin on the Chow ring of hyperkaehler varieties.