Journal of the
Korean Mathematical Society JKMS

It is known that the orbifold Euler characteristic $e_{orb}(S)$ of a log del Pezzo surface $S$ of rank one satisfies the inequality $0 \leq e_{orb}(S) \leq 3$. In this note, we show that the orbifold Euler characteristic of $S$ is strictly positive, i.e., $0 < e_{orb}(S)$. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.

Keywords: log del Pezzo surface of rank one, orbifold Euler characteristic

MSC numbers: Primary 14J26, 14J17