Covers topics such as valuation theory; theory of polynomial and power series rings; and local algebra. This volume includes the algebro-geometric connections and applications of the purely algebraic material.

Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ parameters needed to determine a curve of genus $g$. This book studies the moduli space of curves of the same equisingularity class. It considers the moduli problem fro

The aim of the present monograph is to give a systematic exposition of the theory of algebraic surfaces emphasizing the interrelations between the various aspects of the theory: algebro-geometric, topological and transcendental. To achieve this aim, and still remain inside the limits of the allotted space, it was necessary to confine the exposition to topics which are absolutely fundamental. The present work therefore makes no claim to completeness, but it does, however, cover most of the central points of the theory. A presentation of the theory of surfaces, to be effective at all, must...