2011/10/31 by Pinaki Mondal, Mondal, Pinaki
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.1110.6914
Superseded by "Analytic compactifications of C^2 II: one irreducible curve at infinity"
openalex publication_date 2011/10/31 · arxiv created 2013/07/22 · arxiv updated 2013/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we continue from \citesub2-1 the study of normal analytic compactifications of \cc2 from the point of view of their associated pencils of jets of curve germs centered at infinity. If X is a normal analytic compactification of \cc2 which is \em primitive, i.e. X ∖ \cc2 is irreducible curve, then we show that X is projective iff X is algebraic iff at least one of the jets in the associated pencil of jets of curve-germs can be represented by a planar curve with one place at infinity. As a result we show that there are primitive normal analytic compactifications of \cc2 which are \em not algebraic. We give explicit criteria for determining if the primitive compactification corresponding to a jet of curve germs at infinity is projective or not.