The aim of this book is the study of curves on a smooth projective surface. However, many of the results proved here hold in greater generality. These constitute some of the fundamental theorems in Algebraic Geometry. We find here the construction of the basic geometric objects, such as Grothendieck's Hilbert scheme, the Picard scheme and the Chow schemes. The book also contains the infinitesimal study of the Picard scheme; i.e., the determination of the Zariski ...
