On sums of Betti numbers of affine varieties
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866910795254726656 |
|---|---|
| author | Zhang, Dingxin |
| author_facet | Zhang, Dingxin |
| contents | We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its $\ell$-adic Betti numbers does not exceed $2(N + 1)^{2N +1}(d+ 1)^N$. This answers a question of Katz (FFA 2001). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On sums of Betti numbers of affine varieties Zhang, Dingxin Algebraic Geometry Algebraic Topology 14F25, 14F20 We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its $\ell$-adic Betti numbers does not exceed $2(N + 1)^{2N +1}(d+ 1)^N$. This answers a question of Katz (FFA 2001). |
| title | On sums of Betti numbers of affine varieties |
| topic | Algebraic Geometry Algebraic Topology 14F25, 14F20 |
| url | https://arxiv.org/abs/2411.02970 |