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Plane curves as projections of non singular space curves. (English) Zbl 0728.14030

It is well known that any irreducible projective plane curve \(\Gamma\) can be obtained as a projection of a nonsingular space curve C spanning \({\mathbb{P}}^ r\) (some \(r\geq 3)\), from a linear space which may intersect C. The author revisites the work of Enriques [cf. F. Enriques and O. Chisini, “Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche” (Bologna 1918; Reprint 1985; Zbl 0571.51001); Vol. II, Libro IV, Cap. 4] based on the theory of adjoints and show that we can take \(r=4\) in the above statement, moreover every nonsingular plane curve of degree \( d\) is the projection of a nonsingular curve of degree \( 2d-1\) spanning \({\mathbb{P}}^ 4\) and that no lower degree is possible.

MSC:

14H50 Plane and space curves

Citations:

Zbl 0571.51001
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References:

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