The motive of a variety with cellular resolution of singularities
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909676246925312 |
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| author | Stonek, Bruno |
| author_facet | Stonek, Bruno |
| contents | A complex variety $X$ admits a cellular resolution of singularities if there exists a resolution of singularities $\widetilde X\to X$ such that its exceptional locus as well as $\widetilde X$ and the singular locus of $X$ admit a cellular decomposition. We give a concrete description of the motive with compact support of $X$ in terms of its Borel-Moore homology, under some mild conditions. We give many examples, including rational projective curves and toric varieties of dimension two and three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The motive of a variety with cellular resolution of singularities Stonek, Bruno Algebraic Geometry Algebraic Topology 14F42 (Primary), 14M25, 55N35 (Secondary) A complex variety $X$ admits a cellular resolution of singularities if there exists a resolution of singularities $\widetilde X\to X$ such that its exceptional locus as well as $\widetilde X$ and the singular locus of $X$ admit a cellular decomposition. We give a concrete description of the motive with compact support of $X$ in terms of its Borel-Moore homology, under some mild conditions. We give many examples, including rational projective curves and toric varieties of dimension two and three. |
| title | The motive of a variety with cellular resolution of singularities |
| topic | Algebraic Geometry Algebraic Topology 14F42 (Primary), 14M25, 55N35 (Secondary) |
| url | https://arxiv.org/abs/2408.05766 |