Complete intersection points on general surfaces in \PP³

2008/11/13 by Enrico Carlini, Carlini, E., Luca Chiantini +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0811.2233

openalex publication_date 2008/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the existence of complete intersection points of type (a,b,c), on the generic degree d surface of \PP³. For any choice of a, b, c we resolve the existence question asymptotically, i.e. for all d ≫ 0. For small values of a, b, c we resolve the existence problem completely.

Related

• Complete intersections on general hypersurfaces
• Maximum number of points on intersection of a cubic surface and a non-degenerate Hermitian surface
• Sets of points which project to complete intersections
• Applications of iterated curve blowup to set-theoretic complete intersections in P3
• Smooth curves on projective K3 surfaces