ON PROJECTIONS OF SMOOTH AND NODAL PLANE CURVES

Suppose that C subset of P-2 is a general enough nodal plane curve of degree > 2, nu: (C) over cap -> C is its normalization, and pi: C' -> P-1 is a finite morphism simply ramified over the same set of points as a projection pr(p) circle nu: (C) over cap -> P-1 ,where p is an element of P-2\C (if deg C = 3, one should assume in addition that deg pi not equal 4). We prove that the morphism pi is equivalent to such a project ion 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 Cinsini conjecture re for mappings ramified over duals to general nodal curves of any degree >= 3 except for duals to smooth cubics; this strengthens one of Victor Kulikov's results.