Projective Curves in Algebraic Geometry

Abstract

This thesis began a thorough investigation of the complicated interactions between geometric characteristics and the intrinsic algebraic structures in the world of projective curves.

The focus of the inquiry was a methodical analysis of curve C' in the confined affine plane A to the power 2 (K) , on the field K, has the set of zeros (x, y) of a polynomial f (X,Y) . The curve C' present in the projective plane P to the power 2 (K has the set of zeros (x, y, z) of a polynomial which were homogeneous F (X, Y, Z).

Therefore, this study investigated the singular point, inflection point, genus of C' along with the points of intersections of these two curves and produced valuable results.