Curves in Projective Spaces

Abstract

As we will see below, the projective plane (like any other two-dimensional surface) is too narrow to accommodate every smooth curve. In the three-dimensional space there is much more freedom. However, to define curves in \({\mathbb {C}\mathbb {P}}^3\) and higher dimensional projective spaces is more difficult than in the plane. In this chapter, we discuss methods of defining such curves.