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Regular version of the site

Working paper

On projections of smooth and nodal plane curves

Suppose that C⊂P2 is a general enough smooth plane curve of degree >2 and that π:C→P1 is a finite morphism simply ramified over the same set of points as a projection prp:C→P1, where p∈P2∖C. We prove that the morphism π is equivalent to such a projection if and only if it extends to a finite morphism X→(P2)∗ ramified over C∗, where X is a smooth surface. Actually we prove a similar result for nodal curves.