ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE
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It is known that the orbifold Euler characteristic eorb(S) of a log del Pezzo surface S of rank one satisfies the inequality 0 ≤ eorb(S)≤ 3. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < eorb (S). Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.
Abstract
It is known that the orbifold Euler characteristic eorb(S) of a log del Pezzo surface S of rank one satisfies the inequality 0 ≤ eorb(S)≤ 3. In this note, we show that the orbifold Euler characteristic of S is strictly positive, i.e., 0 < eorb (S). Moreover, we also show, by construction, the existence of log del Pezzo surfaces of rank one with arbitrarily small orbifold Euler characteristic.
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