The Ceresa class: tropical, topological, and algebraic

Abstract: The Ceresa cycle is an algebraic cycle attached to a smooth algebraic curve. It is homologically trivial but not algebraically equivalent to zero for a very general curve. In this sense, it is one of the simplest algebraic cycles that goes ``beyond homology.'' The image of the Ceresa cycle under a certain cycle class map produces a class in étale homology called the Ceresa class. We define the Ceresa class for a tropical curve and for a product of commuting Dehn twists on a topological surface. We relate these to the Ceresa class of a smooth algebraic curve over C((t)). Our main result is that the Ceresa class in each of these settings is torsion. Nevertheless, this class is readily computable, frequently nonzero, and implies nontriviality of the Ceresa cycle when nonzero. This is joint work with Jordan Ellenberg and Wanlin Li.

algebraic geometrycombinatorics

Audience: researchers in the topic

Tropical Geometry in Frankfurt/Zoom TGiF/Z

Series comments: Description: An afternoon seminar series on tropical geometry, known as the TGiZ ("Tropical Geometry in Zoom") or the TGiF ("Tropical Geometry in Frankfurt") seminar.

Please send an email to one of the organizers at the latest one day before a session if you wish to receive the Zoom link and password.

Videos of some past talks are available on YouTube here, while some slides can be found here.