This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories.

Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1.3 Pⁿ 2.1 sheaves of modules; 2.2 vector bundles; 2.3 sheaf cohomology and computations on Pⁿ; 3.1 maximum principle and Schwarz lemma on analytic spaces; 3.2 Siegel's theorem; 3.3 Chow's theorem; 4.1...

This book is a sequel to Lectures on Complex Analytic Varieties: The Local Paranwtrization Theorem (Mathematical Notes 10, 1970). Its unifying theme is the study of local properties of finite analytic mappings between complex analytic varieties; these mappings are those in several dimensions that most closely resemble general complex analytic mappings in one complex dimension. The purpose of this volume is rather to clarify some algebraic aspects of the local study of complex analytic varieties than merely to examine finite analytic mappings for their own sake.

Originally...

This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field.

Originally published in 1972.

The...

Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise.

Originally published in 1970.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of...

Written by Arthur Ogus on the basis of notes from Pierre Berthelot's seminar on crystalline cohomology at Princeton University in the spring of 1974, this book constitutes an informal introduction to a significant branch of algebraic geometry. Specifically, it provides the basic tools used in the study of crystalline cohomology of algebraic varieties in positive characteristic.

Originally published in 1978.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of...

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. Paula Tretkoff emphasizes those finite covers that are free quotients of the complex two-dimensional ball. Tretkoff also includes background on the classical Gauss hypergeometric function of one variable, and a chapter on the Appell two-variable F1 hypergeometric function.

The material in this book began as a set of lecture notes, taken by Tretkoff, of a course given by Friedrich Hirzebruch at ETH Zurich in 1996. The lecture notes...

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems.

Originally published in 1979.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from...

There was a special year devoted to the topic of several complex variables at the Mittag-Leffler Institute in Stockholm, Sweden, and this volume contains the resulting survey papers and research papers. The work covers a broad spectrum of developments in this field. The contributors include H. Alexander; F. Almgren; E. Almar; M. Andersson; E. Bedford; J. Belanger; S. Bell; B. Berndtsson; U. Cegrell; C.H. Chang and H.P. Lee; J. Chaumat and A.M. Chollet; J. D'Angelo; J. P. Demailley; P. Dolbeault; A. Dor; F. Forstneric; B. Gaveau, M. Okada, and T. Okada; R. Greene and S. Krantz; A. Iordan;...

The classical uniformization theorem for Riemann surfaces and its recent extensions can be viewed as introducing special pseudogroup structures, affine or projective structures, on Riemann surfaces. In fact, the additional structures involved can be considered as local forms of the uniformizations of Riemann surfaces. In this study, Robert Gunning discusses the corresponding pseudogroup structures on higher-dimensional complex manifolds, modeled on the theory as developed for Riemann surfaces.

Originally published in 1978.

The Princeton Legacy Library uses the latest...

The theory of D-modules deals with the algebraic aspects of differential equations. These are particularly interesting on homogeneous manifolds, since the infinitesimal action of a Lie algebra consists of differential operators. Hence, it is possible to attach geometric invariants, like the support and the characteristic variety, to representations of Lie groups. By considering D-modules on flag varieties, one obtains a simple classification of all irreducible admissible representations of reductive Lie groups. On the other hand, it is natural to study the representations realized by...