Complete intersections on Veronese surfaces

2022/02/17 by Stefano Canino, Canino, Stefano, Enrico Carlini +1
Computer Science · Engineering · Mathematics · #13D40 #14N05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2202.08565

openalex publication_date 2022/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of the quadratic Veronese threefold. Our main tool is an effective characterization of all possible Hilbert functions of reduced subvarieties of Veronese surfaces.

Related

• A note on the Intersection of Veronese Surfaces
• Counting 3-uple Veronese surfaces
• A classification of planes intersecting the Veronese surface over finite fields of even order
• Criteria for complete intersections
• Simultaneous Diophantine approximation on the three dimensional Veronese curve