2020/10/31 by Lucas das Dores, Dores, Lucas das
Computer Science · #14D22 (Primary) 14H10 (Secondary) #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #Data Visualization and Analytics #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2011.00331
openalex publication_date 2020/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a fixed projective scheme which is flat over a base scheme S. The association taking a quasi-projective S-scheme Y to the scheme parametrizing S-morphisms from X to Y is functorial. We prove that this functor preserves limits, and both open and closed immersions. As an application, we determine a partition of schemes parametrizing rational curves on the blow-ups of projective spaces at finitely many points. We compute the dimensions of its components containing rational curves outside the exceptional divisor and the ones strictly contained in it. Furthermore, we provide an upper bound for the dimension of the irreducible components intersecting the exceptional divisors properly.