Differential forms and cohomology in tropical and complex geometry
Abstract
Ducros, Hrushovski, and Loeser gave maps from families of archimedean diffrential forms to non-archiemedean (or tropical) ones, which are compatible with integrals on algebraic varieties. In this paper, we introduce slight modifications of their maps for complex projective varieties which give natural maps from tropical to the usual Dolbeault cohomology. We also show that our maps are compatible with integrals on generic semi-algebraic subsets and those on their weighted tropicalizations. Weighted tropicalizations induce the dual maps of the above maps of Dolbeault cohomology groups under some assumptions.
Keywords
Cite
@article{arxiv.2106.11479,
title = {Differential forms and cohomology in tropical and complex geometry},
author = {Ryota Mikami},
journal= {arXiv preprint arXiv:2106.11479},
year = {2024}
}
Comments
27 pages, V.4, largely changed, title changed from"Basics of maps from tropical cohomology to singular cohomology": V. 2 and 3, minor changes