Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
A Surface with Representable $CH_{0}$-group but No Universal Zero-cycle
Theodosis Alexandrou (Humboldt-Universität zu Berlin)
Abstract: We introduce a new obstruction to the existence of a universal 0-cycle on a smooth projective complex variety. As an application, we construct a smooth projective complex surface whose Chow group of 0-cycles is representable but which does not admit a universal 0-cycle. This provides a two-dimensional analogue of Voisin’s recent threefold counterexample to a question of Colliot-Thélène. As a further consequence, we exhibit the first example of a smooth projective threefold of Kodaira dimension zero carrying a non-torsion Hodge class of degree 4 that is not algebraic. The construction relies on the geometry of bielliptic surfaces of type 2.
Meeting ID: 869 2196 7919
Passcode: 795622
Organizer: Sasha Viktorova (NCTS)
