On the branch curve of a general projection of a surface to a plane

Ciliberto, C.; Flamini, F.

doi:10.1090/S0002-9947-2011-05401-2

On the branch curve of a general projection of a surface to a plane
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by C. Ciliberto and F. Flamini PDF

Trans. Amer. Math. Soc. 363 (2011), 3457-3471 Request permission

Abstract:

In this paper we prove that the branch curve of a general projection of a surface to the plane is irreducible, with only nodes and cusps. This is a basic result in surface theory, extremely useful in various applications. However, its proof, in this general setting, was so far lacking. Our approach substantially uses a powerful tool from projective differential geometry, i.e., the concept of focal schemes.

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