Global F-regularity for weak del Pezzo surfaces

Kawakami, Tatsuro  ; Tanaka, Hiromu 

Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e77

Résumé

Let k be an algebraically closed field of characteristic $p>0$. Let X be a normal projective surface over k with canonical singularities whose anticanonical divisor is nef and big. We prove that X is globally F-regular except for the following cases: (1) $K_X^2=4$ and $p=2$, (2) $K_X^2=3$ and $p \in \{2, 3\}$, (3) $K_X^2=2$ and $p \in \{2, 3\}$, (4) $K_X^2=1$ and $p \in \{2, 3, 5\}$. For each degree $K_X^2$, the assumption of p is optimal.

Détail

DOI : 10.1017/fms.2024.143

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