Title: ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE
Abstract:It is known that the orbifold Euler characteristic <TEX>$e_{orb}(S)$</TEX> of a log del Pezzo surface S of rank one satisfies the inequality <TEX>$0{\leq}e_{orb}(S){\leq}3$</TEX>. In this note, we sho...It is known that the orbifold Euler characteristic <TEX>$e_{orb}(S)$</TEX> of a log del Pezzo surface S of rank one satisfies the inequality <TEX>$0{\leq}e_{orb}(S){\leq}3$</TEX>. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < <TEX>$e_{orb}(S)$</TEX>. Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.Read More