2000 character limit reached
On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension (2507.01797v1)
Published 2 Jul 2025 in math.AG
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.