Enumeration of surfaces containing an elliptic quartic curve

A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain some elliptic quartic curve. We also compute the degree of...

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Bibliographic Details
Published in:arXiv.org 2014-07
Main Authors: Cukierman, Fernando, Lopez, Angelo, Vainsencher, Israel
Format: Article
Language:English
Subjects:
Enumeration
Intersections
Loci
Online Access:Get full text
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Summary:A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain some elliptic quartic curve. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula.
ISSN:2331-8422