On Tropical Intersection Theory

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.

arXiv comment22 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 (§2.4, Def. 3.4)