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.