Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class
Algebraic Geometry
2020-12-25 v1 Combinatorics
Complex Variables
Differential Geometry
Geometric Topology
Abstract
This is a sequel to our work in tropical Hodge theory. Our aim here is to prove a tropical analogue of the Clemens-Schmid exact sequence in asymptotic Hodge theory. As an application of this result, we prove the tropical Hodge conjecture for smooth projective tropical varieties which are rationally triangulable. This provides a partial answer to a question of Kontsevich who suggested the validity of the tropical Hodge conjecture could be used as a test for the validity of the Hodge conjecture.
Keywords
Cite
@article{arxiv.2012.13142,
title = {Tropical Clemens-Schmid sequence and existence of tropical cycles with a given cohomology class},
author = {Omid Amini and Matthieu Piquerez},
journal= {arXiv preprint arXiv:2012.13142},
year = {2020}
}
Comments
32 pages, 8 figures