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arXiv · 2408.12417

Dimensionality of tropical Chow groups

Álvaro Muñiz-Brea
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Abstract

We show that the existence of non-zero tropical forms of degree at least two implies that the tropical Chow group of points of a tropical affine manifold is infinite-dimensional. This can be seen as a tropical analog of classical results of Mumford and Roitman for Chow groups of smooth (complex) projective algebraic varieties. We also show that the existence of tropical 1-forms on tropical surfaces does not imply infinite dimensionality by considering the case of a tropical Klein bottle.

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BibTeXRIS

Álvaro Muñiz-Brea. 2026-07-16. Dimensionality of tropical Chow groups. https://doi.org/10.1017/prm.2026.10165

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