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arXiv · 2107.12067

On Tropical Intersection Theory

Andreas Mihatsch
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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.

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Andreas Mihatsch. 2021-07-26. On Tropical Intersection Theory. https://arxiv.org/abs/2107.12067

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