|Topology of Algebraic Varieties|
|Topic:||Chow rings and modified diagonals|
|Affiliation:||Sapienza - Università di Roma; Member, School of Mathematics|
|Date:||Tuesday, October 7|
|Time/Room:||2:00pm - 3:00pm/S-101|
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.