Rational curves on complete intersections and the circle method

2024/04/17 by T. D. Browning, Browning, Tim, Pankaj Vishe +3 · 2 citations
Computer Science · Engineering · Mathematics · #11P55 #14G05 #14H10 (11D45 #14J70) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.11123

openalex publication_date 2024/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the geometry of the space of rational curves on smooth complete intersections of low degree, which pass through a given set of points on the variety. The argument uses spreading out to a finite field, together with an adaptation to function fields of positive characteristic of work by Rydin Myerson on the circle method. Our work also allows us to handle weak approximation for such varieties.

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