# ON THE ORBIFOLD EULER CHARACTERISTIC OF LOG DEL PEZZO SURFACES OF RANK ONE

• Received : 2014.04.07
• Published : 2014.07.01

#### Abstract

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.

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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