Enumeration of surfaces containing an elliptic quartic curve
Algebraic Geometry
2014-07-09 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1209.3335,
title = {Enumeration of surfaces containing an elliptic quartic curve},
author = {Fernando Cukierman and Angelo Lopez and Israel Vainsencher},
journal= {arXiv preprint arXiv:1209.3335},
year = {2014}
}
Comments
Minor typos corrected. To appear on Proceedings of the American Mathematical Society