On complete intersections and connectedness

Abstract

In this thesis, we study the relation between connectedness and complete intersections. We describe the concept of connectedness in codimension k. We also study the basic facts about Cohen-Macaulay rings, and give some applications about these rings and complete intersections. Finally, we show that certain rational curves of degree ≥ 4 in the projective 3-space are settheoretical complete intersections in all prime characteristics p > 0.