2019/10/08 by Gene Freudenburg, Hideo Kojima, Freudenburg, Gene +3 · 1 citation
Mathematics · #14J26 #14R05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1910.03494
openalex publication_date 2019/10/08 · openalex created_date 2019/10/18 · openalex updated_date 2026/07/28
This paper considers the family \mathscrS0 of smooth affine factorial surfaces of logarithmic Kodaira dimension 0 with trivial units over an algebraically closed field k. Our main result (Theorem 4.1) is that the number of isomorphism classes represented in \mathscrS0 is at least countably infinite. This contradicts the earlier classification of Gurjar and Miyanishi [5] which asserted that \mathscrS0 has at most two elements up to isomorphism when k=ℂ. Thus, the classification of surfaces in \mathscrS0 for the field ℂ, long thought to have been settled, is an open problem.