Algebraic cycles on surfaces and related conjectures

Cycle 31th Seminar for the admission at final exam

July 23, 2019
Versione stampabile
Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 11.30 a.m.
  • Natascia Zangani - PhD in Mathematics
Abstract:
In the spirit of investigating the conjectural influence of singular cohomology on Chow groups, in 1996 C. Voisin formulated a conjecture about 0-cycles on surfaces. This conjecture arises in the context of the Bloch-Beilinson’s conjecture, and it has been verified in some specific cases where an explicit description of the surfaces was available. Despite these results, the conjecture is still open for a general K3 surface. We focus on the family of Todorov surfaces of type (2,12), presenting an explicit description of it in terms of complete intersections and quotients by a group action. We prove Voisin’s conjecture for this family and we present a motivic version of this result and some related applications.
 
Supervisor: Claudio Fontanari