Characteristic numbers of ellitpic space curves with fixed j-invariant

Details Characteristic numbers of ellitpic space curves with fixed j-invariant Characteristic numbers of ellitpic space curves with fixed j-invariant

2011-11-27

arxiv.org/abs/1111.6295v2

Mathematics

Algebraic Geometry

4 figures, 18 tables. arXiv admin note: substantial text overlap with arXiv:1102.0827 and arXiv:1012.1674

Scientific paper

We solve the problem of counting elliptic curves with fixed j-invariant in projective space with tangency conditions. This is equivalent to couting rational nodal curves with condition on the node of the image. The solution is given in the form of effective recursions. We give explicit formulas when the dimension of the ambient projective space is at most 5. Many numerical examples are provided. A C++ program implementing most of the recursions is available on the author's webpage (see \cite{dn}).

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