Interpolation for degree 2 Veroneses of odd dimension

2024/11/25 by R. Shang, Shang, Ray
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2411.16672

openalex publication_date 2024/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical fact is that through any d+3 general points in ℙ_ℂ^d there exists a unique rational normal curve of degree d passing through them. We generalize this by proving the following: when n is odd, for any \binomn+22 + n+1 general points in ℙ_ℂ^\binomn+22 - 1, there exist at least 2^n(n-1) degree 2 Veroneses passing through them. This makes substantial progress on a question of Aaron Landesman and Anand Patel, and extends the work of Arthur Coble.

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