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Regular version of the site

Article

On projections of smooth and nodal plane curves

Moscow Mathematical Journal. 2015. Vol. 15. No. 1. P. 31-48.

Suppose that C ⊂ P^2 is a general enough nodal plane curve
of degree > 2,  :  \hat C → C is its normalization, and  π: C′ → P^1 is a finite
morphism simply ramified over the same set of points as a projection
pr_p ◦ν  : \hat C → P1, where p ∈ P^2 \ C (if degC = 3, one should assume in
addition that deg  6= 4). We prove that the morphism  is equivalent to
such a projection if and only if it extends to a finite morphism X → (P^2)^∗
ramified over C^∗, where X is a smooth surface.
As a by-product, we prove the Chisini conjecture for mappings ram-
ified over duals to general nodal curves of any degree > 3 except for
duals to smooth cubics; this strengthens one of Victor Kulikov’s results.