Dimensionality of tropical Chow groups
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909293597425664 |
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| author | Muñiz-Brea, Álvaro |
| author_facet | Muñiz-Brea, Álvaro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12417 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimensionality of tropical Chow groups Muñiz-Brea, Álvaro Algebraic Geometry 14C15, 14T99 (Primary) 14T20 (Secondary) 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. |
| title | Dimensionality of tropical Chow groups |
| topic | Algebraic Geometry 14C15, 14T99 (Primary) 14T20 (Secondary) |
| url | https://arxiv.org/abs/2408.12417 |