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Enumeration of surfaces containing an elliptic quartic curve


Authors: F. Cukierman, A. F. Lopez and I. Vainsencher
Journal: Proc. Amer. Math. Soc. 142 (2014), 3305-3313
MSC (2010): Primary 14N05, 14N15; Secondary 14C05
DOI: https://doi.org/10.1090/S0002-9939-2014-11998-8
Published electronically: July 8, 2014
MathSciNet review: 3238408
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Abstract: A very general surface of degree at least four in $ \mathbb{P}^{3}$ contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces in $ \mathbb{P}^{3}$ of degree at least five which contain some elliptic quartic curves. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula.


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Additional Information

F. Cukierman
Affiliation: Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, (1428) Buenos Aires, Argentina
Email: fcukier@dm.uba.ar

A. F. Lopez
Affiliation: Dipartimento di Matematica e Fisica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy
Email: lopez@mat.uniroma3.it

I. Vainsencher
Affiliation: ICEX-Departamento de Matemática-UFMG, Av. Antônio Carlos, 6627 – Caixa Postal 702, CEP 31270-901 Belo Horizonte, MG, Brazil
Email: israel@mat.ufmg.br

DOI: https://doi.org/10.1090/S0002-9939-2014-11998-8
Keywords: Intersection theory, Noether-Lefschetz locus, enumerative geometry
Received by editor(s): November 15, 2011
Received by editor(s) in revised form: August 20, 2012, and September 19, 2012
Published electronically: July 8, 2014
Additional Notes: The first author was partially supported by CONICET-Argentina.
The second author was partially supported by PRIN Geometria delle varietà algebriche e dei loro spazi di moduli.
The third author was partially supported by CNPQ-Brasil.
Dedicated: Dedicated to Steve Kleiman on the occasion of his 70th birthday
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.