On projections of smooth and nodal plane curves

الأصل · EN

Suppose that C² is a general enough nodal plane curve of degree >2, ν C→ C is its normalization, and π C¹ is a finite morphism simply ramified over the same set of points as a projection prₚ∘ ν C ¹, where p² C (if deg C=3, one should assume in addition that π≠4). 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. As a by-product, we prove the Chisini conjecture 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.