The present monograph grew out of the fifth set of Hermann Weyl Lectures, given by Professor Griffiths at the Institute for Advanced Study, Princeton, in fall 1974.

In Chapter 1 the author discusses Emile Borel's proof and the classical Jensen theorem, order of growth of entire analytic sets, order functions for entire holomorphic mappings, classical indicators of orders of growth, and entire functions and varieties of finite order.

Chapter 2 is devoted to the appearance of curvature, and Chapter 3 considers the defect relations. The author considers the lemma on the...

The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is...

In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles.

The book...