2011/11/27 by Dung Tien Nguyen, Dung Nguyen, Nguyen, Dung
Mathematics · #14-XX #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #math.AG #msc:14-XX
paper · pdf · doi:10.48550/arxiv.1111.6295
4 figures, 18 tables. arXiv admin note: substantial text overlap with arXiv:1102.0827 and arXiv:1012.1674
openalex publication_date 2011/11/27 · arxiv created 2011/11/29 · arxiv updated 2011/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citedn).