Chow theory of toric variety bundles
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866918232571510784 |
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| author | Carocci, Francesca Monin, Leonid Nabijou, Navid |
| author_facet | Carocci, Francesca Monin, Leonid Nabijou, Navid |
| contents | We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the ordinary cohomology with homology-valued Minkowski weights, and identify the equivariant cohomology with cohomology-weighted piecewise polynomial functions. We describe the product structure on Minkowski weights via a fan displacement rule, and the non-equivariant limit via equivariant multiplicities. Along the way we establish relative analogues of the Künneth property and Kronecker duality. Applications include the balancing condition in logarithmic enumerative geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16883 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chow theory of toric variety bundles Carocci, Francesca Monin, Leonid Nabijou, Navid Algebraic Geometry 14M25, 14D06, 14C15, 14C17 We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the ordinary cohomology with homology-valued Minkowski weights, and identify the equivariant cohomology with cohomology-weighted piecewise polynomial functions. We describe the product structure on Minkowski weights via a fan displacement rule, and the non-equivariant limit via equivariant multiplicities. Along the way we establish relative analogues of the Künneth property and Kronecker duality. Applications include the balancing condition in logarithmic enumerative geometry. |
| title | Chow theory of toric variety bundles |
| topic | Algebraic Geometry 14M25, 14D06, 14C15, 14C17 |
| url | https://arxiv.org/abs/2411.16883 |