Algebraic versus homological equivalence of algebraic cycles
Organizers
Speaker
Arnaud Beauville
Time
Thursday, October 17, 2024 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
An algebraic cycle on a smooth projective variety is algebraically trivial if it can be deformed algebraically to zero. This implies that its cohomology class is zero; in 1969 Griffiths showed that the converse is false for many hypersurfaces. A different example is constructed from a curve C embedded in its Jacobian JC : the "Ceresa cycle" [C] - [(-1)*C] in JC is not algebraically trivial if C is general (Ceresa, 1983), while it is if C is hyperelliptic. In the last three years a number of approaches have been developed to find non-hyperelliptic curves for which this cycle is algebraically trivial.
In the talk I will survey the history of the problem, then discuss these recent examples of non-hyperelliptic curves, in particular the approach of Laga and Shnidman (2024).
In the talk I will survey the history of the problem, then discuss these recent examples of non-hyperelliptic curves, in particular the approach of Laga and Shnidman (2024).