Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: C. Ciliberto and F. Flamini
Journal: Trans. Amer. Math. Soc. 363 (2011), 3457-3471
MSC (2010): Primary 14N05, 14E20, 14E22; Secondary 14J10, 14E05
Published electronically: February 8, 2011
MathSciNet review: 2775814
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14N05, 14E20, 14E22, 14J10, 14E05

Retrieve articles in all journals with MSC (2010): 14N05, 14E20, 14E22, 14J10, 14E05


Additional Information

C. Ciliberto
Affiliation: Dipartimento di Matematica, Università degli Studi di Roma Tor Vergata, Via della Ricerca Scientifica, 00133 Roma, Italy
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
Email: flamini@mat.uniroma2.it

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05401-2
PII: S 0002-9947(2011)05401-2
Keywords: Projective surfaces, general projections, coverings, branch curves, singularities.
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”.
Article copyright: © Copyright 2011 American Mathematical Society