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arXiv · 2411.02970

On sums of Betti numbers of affine varieties

Dingxin Zhang
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Abstract

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).

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Dingxin Zhang. 2024-11-05. On sums of Betti numbers of affine varieties. https://doi.org/10.1016/j.ffa.2025.102583

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