Nollet, ScottAguirre, Luis G.2018-05-162018-05-1620182018https://repository.tcu.edu/handle/116099117/21823We study non-reduced locally Cohen-Macaulay quasi-primitive curves supported on a line in three dimensional projective space over an algebraically closed field k. For an odd prime p, we determine exactly when two extremal p-fold lines W and V are directly linked. In particular, W is self-linked if and only if char k = 2, analogous to Migliores result for p=2. The results hold for multiple lines of any degree if we add the extra hypothesis of using quadric surfaces to do the linking. We provide a complete analysis for triple lines.1 online resource (iv, 131 pages).Format: OnlineengNo search engine accessGeometry, Algebraic.Cohen-Macaulay rings.Commutative algebra.Forms, Quadratic.Text