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.
Ciliberto, C., Flamini, F. (2011). On the branch curve of a general projection of a surface to a plane. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(7), 3457-3471 [10.1090/S0002-9947-2011-05401-2].
On the branch curve of a general projection of a surface to a plane
CILIBERTO, CIRO;FLAMINI, FLAMINIO
2011-07-08
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.File in questo prodotto:
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