On Tropical Intersection Theory
Algebraic Geometry
2022-08-30 v3
Abstract
We develop a tropical intersection formalism of forms and currents that extends classical tropical intersection theory in two ways. First, it allows to work with arbitrary polytopes, also non-rational ones. Second, it allows for smooth differential forms as coefficients. The intersection product in our formalism can be defined through the diagonal intersection method of Allermann--Rau or the fan displacement rule. We prove with a limiting argument that both definitions agree.
Keywords
Cite
@article{arxiv.2107.12067,
title = {On Tropical Intersection Theory},
author = {Andreas Mihatsch},
journal= {arXiv preprint arXiv:2107.12067},
year = {2022}
}
Comments
22 pages, two noteworthy changes: added the definition of pullback for non-surjective maps (Def. 4.2), changed the sign of the boundary integral and boundary operator to conform with the literature convention ({\S}2.4, Def. 3.4)