Global F-regularity for weak del Pezzo surfaces

Abstract

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.

Keywords

• 14J45
• 13A35