Complete intersection points on general surfaces in $\PP^3$

TL;DR

This paper investigates the existence of complete intersection points of type (a,b,c) on generic degree d surfaces in projective 3-space, providing asymptotic results for large d and complete solutions for small parameters.

Contribution

It offers asymptotic existence results for all (a,b,c) and complete solutions for small values, advancing understanding of intersection points on surfaces in projective space.

Findings

Asymptotic existence of (a,b,c) points for large d

Complete solutions for small (a,b,c) values

Resolution of the existence problem in specific cases

Abstract

In this paper we consider the existence of complete intersection points of type $(a,b,c)$, on the generic degree $d$ surface of $\PP^3$. For any choice of $a, b, c$ we resolve the existence question asymptotically, i.e. for all $d \gg 0$. For small values of $a, b, c$ we resolve the existence problem completely.