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Oscar Zariski’s work in mathematics permanently altered the foundations of algebraic geometry. The powerful tools he forged from the ideas of modern algebra allowed him to penetrate classical problems with an unaccustomed depth, and brought new rigor to the intuitive proofs of the Italian School. The students he trained at Hopkins, and later at Harvard, are among the foremost mathematicians of our time.

While what he called his “real life” is recorded in almost a hundred books and papers, this story of his “unreal life” is based upon Parikh’s interviews with his family, colleagues, and students, and on his own memories from a series of tape-recorded interviews made a few years before his death in 1986.

First published in 1991, The Unreal Life of Oscar Zariski was highly successful and widely praised, but has been out of print for many years. Springer is proud to make this book available again, introducing Oscar Zariski to a new generation of mathematicians.

Customer Reviews (1)

A Mathematician in Turbulent Times
Carol Parikh's engaging bio of Oscar Zariski is a valuable contribution to the history of mathematics; it provides an understandable history of the development of algebraic geometry. The book also offers a valuable lesson in how political and racist vendettas have affected the "pure" science of mathematics and the lives of mathematicians. I came across her compelling book a year after publishing "A3 & His Algebra," the bio of A.A. Albert, who had a close collegial relationship with Zariski. The personal histories of both men demonstrate the importance of a free and open academic atmosphere to the development of scientific innovation.Nancy E. Albert, author of "A3 & His Algebra". ... Read more

Product Description
This is the second of four volumes that will eventually present the full corpus of Zariski's mathematical contribution. Like the first volume (subtitled Foundations of Algebraic Geometry and Resolution of Singularities, and edited by H. Hironaka and D. Mumford), it is divided into two parts, each devoted to a large but circumscribed area of research activity.

The first part, containing eight papers introduced by Artin, deals with the theory of formal holomorphic functions on algebraic varieties over fields of any characteristic. The primary concern, in Zariski's words, is "analytic properties of an algebraic variety V, either in the neighborhood of a point (strictly local theory) or—and this is the deeper aspect of the theory—in the neighborhood of an algebraic sub-variety of V (semiglobal theory)."

Mumford surveys the ten papers reprinted in the second part. These deal with linear systems and the Riemann-Roch theorem and its applications, again in arbitrary characteristic. The applications are primarily to algebraic surfaces and include minimal models and characterization of rational or ruled surfaces. ... Read more

Product Description
Oscar Zariski's earliest papers originally appeared in 1924 and have been followed by a steady accretion ever since. That at least four volumes are required to publish his collected papers is an index to his productiveness and persistence; that they have been collected at all is a tribute to their continuing importance in the field of algebraic geometry.

The first two volumes of Zariski's papers were published in 1973. Volume I, Foundations of Algebraic Geometry and Resolution of Singularities, was edited by H. Hironaka and D. Mumford, and Volume II, Holomorphic Functions and Linear Systems, was edited by M. Artin and D. Mumford.

The papers contained in this third volume were originally published between 1925 and 1966, but the heart of the book is a sequence of papers, topological in nature, that appeared during the period 1928-1937. Zariski writes that "the reader will find in the introduction by M. Artin and B. Mazur an illuminating discussion of these papers and of their impact on later work by other mathematicians. Their discussion includes, in particular, my papers dealing with the following three topics: (1) solvability in radicals of equations of certain plane curves; (2) the fundamental group of the residual space of plane algebraic curves; (3) the topology of the singularities of plane algebraic curves."

M. Artin (of MIT) and B. Mazur (of Harvard) both studied under Zariski at Harvard and have since become his colleagues. Their Introduction to this volume provides a useful perspective on Zariski's topological work and on this area of topology in general.

These volumes are included in the series Mathematicians of Our Time, under the general editorship of Gian-Carlo Rota. Other volumes in the series now published include papers by Paul Erdös, Einar Hille, Charles Loewner, Percy Alexander MacMahon, George Pólya, Hans Rademacher, Stanislaw Ulam, and Norbert Wiener. ... Read more

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Oscar Zariski, one of the most eminent mathematicians of our time, climaxed a distinguished career by receiving the National Medal of Science. He has enriched mathematics, particularly in algebraic geometry and modern algebra, by numerous and fundamental papers. This volume is the first of four in which these papers are available in collected form.

By introducing ideas from abstract algebra into algebraic geometry, Zariski undertook to rewrite its foundations completely, taking an approach that made no use whatsoever of topological or convergent power series methods and that made no appeal to vague geometric intuition. The most important characteristic of this approach toward algebraic geometry, and in particular toward the problem of resolution of singularities, is that it uses the available power of modern algebra as fully as possible not only as a source of techniques in each step of solving a specific problem but also in reformulating the problem at a fundamental level. Professor Hironaka writes, "By this type of fundamental approach (not to mention specific techniques he invented to overcome specific difficulties in the problem), he made it much easier for other mathematicians in later works to follow the tracks and make further progress."

The present work contains 10 papers on foundations and 9 on the resolution of singularities that were first published between 1937 and 1967. In them, new methods are introduced that enabled Zariski to study algebraic geometry over arbitrary fields of coefficients. This broader outlook made it possible to solve certain classical problems using ideal theory and the theory of valuations that had long been regarded as too difficult to be handled.

Among the basic problems whose solution is found in these papers are the local uniformization of all algebraic varieties, the reduction of singularities of 2- and 3-dimensional varieties, the introduction of the concept of normal variety which is now universally used, and the proof of "Zariski's Main Theorem."

Oscar Zariski: Collected Papers is part of the series Mathematicians of Our Time, edited by Gian-Carlo Rota. ... Read more

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In September 1997, the Working Week on Resolution of Singularities was held at Obergurgi in the Tyrolean Alps. Its objective was to manifest the state of the art in the field and to formulate major questions for future research. The four courses given during this week were written up by the speakers and make up Part I of this volume. They are complemented in Part II by fifteen selected contributions on specific topics and resolution theories.

The volume is intended to provide a broad and accessible introduction to resolution of singularities leading the reader directly to concrete research problems.

Series: Progress in Mathematics, Vol. 181 ... Read more

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Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ parameters needed to determine a curve of genus $g$. In this book, Zariski studies the moduli space of curves of the same equisingularity class. After setting up and reviewing the basic material, Zariski devotes one chapter to the topology of the moduli space, including an explicit determination of the rare cases when the space is compact. Chapter V looks at specific examples where the dimension of the generic component can be determined through rather concrete methods. Zariski's last chapter concerns the application of deformation theory to the moduli problem, including the determination of the dimension of the generic component for a particular family of curves.An appendix by Bernard Teissier reconsiders the moduli problem from the point of view of deformation theory. He gives new proofs of some of Zariski's results, as well as a natural construction of a compactification of the moduli space. ... Read more

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From the Preface: "We have preferred to write a self-contained book which could be used in a basic graduate course of modern algebra. It is also with an eye to the student that we have tried to give full and detailed explanations in the proofs... We have also tried, this time with an eye to both the student and the mature mathematician, to give a many-sided treatment of our topics, not hesitating to offer several proofs of one and the same result when we thought that something might be learned, as to methods, from each of the proofs." ... Read more

Customer Reviews (2)

Old writting style and no exercises
I just bought this book to have it in my desk. I already have the books by Atiyah+MacDonald and Matsumura on commutative algebra and recommend them over this one. However, I always wanted to have this classic that's supposed to be the first text on commutative algebra on print (as fas as I know). As fas as I've noticed there are two things I don't like about the book:

1) It's written in an old and (now considered) informal style. For example chapter 1 starts with "Let G be an arbitrary set of elements a,b,c..."and then, when talking about the group operation on G, quotes the elements a,b,c.

2)It lacks exercises. A good book should have plenty of excercises to help the student to fully understand the new topics.

Aside from this points, I think the book is pretty good and am glad to have it as a reference. Also, this book starts from zero, assuming the reader has no knowledge on groups. The real "commutative algebra" stuff starts on chapter 3 "ideals and modules". If you want to learn commutative algebra, start with the book by Atiyah and MacDonald (of course after having a basic course on Groups, Rings and Fields). I also recommend Matsumura's book after Atiyah-MacDonald, although it was hard to me as a beginner. After that, if you are still interested, this book works as a reference, not as a text.

Not much to say, really.
I bought this to have a matching set with my Volume II.
Decent enough for reference, but that's about it.
Yeah...that's about it. ... Read more

Product Description
The main aim of this book is to present a completely algebraic approach to the Enriques' classification of smooth projective surfaces defined over an algebraically closed field of arbitrary characteristic. This algebraic approach is one of the novelties of this book among the other modern textbooks devoted to this subject. Two chapters on surface singularities are also included. The book can be useful as a textbook for a graduate course on surfaces, for researchers or graduate students in algebraic geometry, as well as those mathematicians working in algebraic geometry or related fields. ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 112 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more