Objects of classical algebraic geometry and ringed spaces

Abstract

Classical Algebraic Geometry can be defined as the study quasiaffine and quasiprojective varieties over a field k. One of the main problems in this area is the classification of these objects modulo isomorphism. These varieties are subsets of affine n- espace, and subsets of complex projective n- space, respectively. It is important to define these objects intrinsecally, tha is, not as part of some ambient space. In this article it is shown how the notion of Ringed Space is the key to formulate such definitions and classification problem.