On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension

Jefferson Baudin

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arXiv · 2507.01797

On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension

Jefferson Baudin

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Abstract

We show that a smooth proper weakly ordinary variety $X$ of maximal Albanese dimension satisfies $\chi(X, \omega_X) \geq 0$. We also show that if $X$ is not of general type, then $\chi(X, \omega_X) = 0$ and the Albanese image of $X$ is fibered by abelian varieties. The proof uses the positive characteristic generic vanishing theory developed by Hacon-Patakfalvi, as well as our recent Witt vector version of Grauert-Riemenschneider vanishing.

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Jefferson Baudin. 2025-07-02. On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension. https://arxiv.org/abs/2507.01797

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