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
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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.References
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Additional Information
- C. Ciliberto
- Affiliation: Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy
- MR Author ID: 49480
- Email: cilibert@mat.uniroma2.it
- F. Flamini
- Affiliation: Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy
- MR Author ID: 650600
- Email: flamini@mat.uniroma2.it
- Received by editor(s): February 9, 2009
- Published electronically: February 8, 2011
- Additional Notes: The authors are members of G.N.S.A.G.A. at I.N.d.A.M. “Francesco Severi”.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 3457-3471
- MSC (2010): Primary 14N05, 14E20, 14E22; Secondary 14J10, 14E05
- DOI: https://doi.org/10.1090/S0002-9947-2011-05401-2
- MathSciNet review: 2775814