2012/11/19 by Pinaki Mondal, Mondal, Pinaki · 1 citation
Computer Science · Mathematics · #14E15 #14J17 #32S25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E15 #msc:14J17 #msc:32S25
paper · pdf · doi:10.48550/arxiv.1211.4333
20 pages, 6 figures
arxiv created 2012/11/19 · openalex publication_date 2012/11/19 · arxiv updated 2012/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a novel and effective criterion for algebraicity of rational normal analytic surfaces constructed from resolving the singularity of an irreducible curve-germ on CP2 and contracting the strict transform of a given line and all but the `last' of the exceptional divisors. As a by-product we construct a new class of analytic non-algebraic rational normal surfaces which are `very close' to being algebraic. These results are local reformulations of some results in (Mondal, 2011) which sets up a correspondence between normal algebraic compactifications of C2 with one irreducible curve at infinity and algebraic curves in C2 with one place at infinity. This article is meant partly to be an exposition to (Mondal, 2011) and we give a proof of the correspondence theorem of (Mondal, 2011) in the `first non-trivial case'.