In this paper we show that a neighborhood of a point $s$ in a normal complex surface $S$ which admits a projection to the complex plane with branch curve $x^n=y^m$ is obtained by a contracting a section of a ruled surface and quotienting by the action of a finite group. From this description, we are able to find numerical criteria for the rationality and smoothness of the germ $(s,S)$.
Ruled surfaces and generic coverings
MANFREDINI, SANDRO;
2006-01-01
Abstract
In this paper we show that a neighborhood of a point $s$ in a normal complex surface $S$ which admits a projection to the complex plane with branch curve $x^n=y^m$ is obtained by a contracting a section of a ruled surface and quotienting by the action of a finite group. From this description, we are able to find numerical criteria for the rationality and smoothness of the germ $(s,S)$.File in questo prodotto:
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