2013/01/01 by Pinaki Mondal, Mondal, Pinaki
Computer Science · Mathematics · #14E15 #14J26 #32J05 #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:14J26 #msc:32J05
paper · pdf · doi:10.48550/arxiv.1301.0126
5 figures, 12 + 30 pages (the first part introduction and statements of results, the second part proofs). Any comments would be greatly appreciated. arXiv admin note: text overlap with arXiv:1211.4333
arxiv created 2013/01/01 · openalex publication_date 2013/01/01 · arxiv updated 2013/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f: Y -> CP2 be a birational morphism of non-singular (rational) surfaces. We give an effective (necessary and sufficient) criterion for algebraicity of the surfaces resulting from contraction of the union of the strict transform of a line on CP2 and all but one of the exceptional divisors of f. As a by-product we construct normal non-algebraic Moishezon surfaces with the `simplest possible' singularities, which in particular completes the answer to a remark of Grauert. Our criterion involves `global variants' of `key polynomials' introduced by MacLane. The geometric formulation of the criterion yields a correspondence between normal algebraic compactifications of C2 with one irreducible curve at infinity and algebraic curves in C2 with one place at infinity.