2016/05/03 by Aaron Landesman, Anand Patel, Landesman, Aaron +1
Computer Science · Engineering · Mathematics · #14J26 #14J45 #14N05 #14N10 #14N25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1605.01117
openalex publication_date 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a rational normal curve in \mathbb Pn through n+3 general points. More recently, it was shown that one can always find nonspecial curves through the expected number of general points and linear spaces. After some expository material regarding scrolls, we consider the generalization of this question to varieties of all dimensions and explain why smooth varieties of minimal degree satisfy interpolation. We give twenty-two equivalent formulations of interpolation. We also classify when Castelnuovo curves satisfy weak interpolation. In the appendix, we prove that del Pezzo surfaces satisfy weak interpolation. Our techniques for proving interpolation include deformation theory, degeneration and specialization, and association.