




OverviewLet me begin with a little history. In the 20th century, algebraic geometry has gone through at least 3 distinct phases. In the period 19001930, largely under the leadership of the 3 Italians, Castelnuovo, Enriques and Severi, the subject grew immensely. In particular, what the late 19th century had done for curves, this period did for surfaces: a deep and systematic theory of surfaces was created. Moreover, the links between the synthetic or purely algebrogeometric techniques for studying surfaces, and the topological and analytic techniques were thoroughly explored. However the very diversity of tools available and the richness of the intuitively appealing geometric picture that was built up, led this school into shortcutting the fine details of all proofs and ignoring at times the time consuming analysis of special cases (e. g., possibly degenerate configurations in a construction). This is the traditional difficulty of geometry, from High School Euclidean geometry on up. In the period 19301960, under the leadership of Zariski, Weil, and (towards the end) Grothendieck, an immense program was launched to introduce systematically the tools of commutative algebra into algebraic geometry and to find a common language in which to talk, for instance, of projective varieties over characteristic p fields as well as over the complex numbers. In fact, the goal, which really goes back to Kronecker, was to create a geometry incorporating at least formally arithmetic as well as projective geo metry. Full Product DetailsAuthor: D Mumford , David Mumford, QC (Boston College Massachusetts)Publisher: SpringerVerlag Berlin and Heidelberg GmbH & Co. KG Imprint: SpringerVerlag Berlin and Heidelberg GmbH & Co. K Edition: 1976. Corr. 2nd Printing ed. Volume: 221 Weight: 0.560kg ISBN: 9783540076032ISBN 10: 3540076034 Pages: 196 Publication Date: 01 May 1981 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsReviewsIn the 20th century, algebraic geometry has undergone several revolutionary changes with respect to its conceptual foundations, technical framework, and intertwining with other branches of mathematics. Accordingly the way it is taught has gone through distinct phases. The theory of algebraic schemes, together with its fullblown machinery of sheaves and their cohomology, being for now the ultimate stage of this evolution process in algebraic geometry, had created  around 1960  the urgent demand for new textbooks reflecting these developments and (henceforth) various facets of algebraic geometry. ... It was David Mumford, who at first started the project of writing a textbook on algebraic geometry in its new setting. His mimeographed Harvard notes ntroduction to algebraic geometry: Preliminary version of the first three chapters (bound in red) were distributed in the mid 1960's, and they were intended as the first stage of a forthcoming, more inclusive textbook. For some years, these mimeographed notes represented the almost only, however utmost convenient and abundant source for nonexperts to get acquainted with the basic new concepts and ideas of modern algebraic geometry. Their timeless utility, in this regard, becomes apparent from the fact that two reprints of them have appeared, since 1988, as a proper book under the title he red book of varieties and schemes' ( Lect. Notes Math. 1358). In the process of exending his Harvard notes to a comprehensive textbook, the author's teaching experiences led him to the didactic conclusion that it would be better to split the book into two volumes, thereby starting with complex projective varieties (in volume I), and proceeding with schemes and their cohomology (in volume II).  In 1976, the author published the first volume under the title lgebraic geometry. I: Complex projective varieties where the corrections concerned the wiping out of some misprints, inconsistent notations, and other slight inaccuracies.The book under review is an unchanged reprint of this corrected second edition from 1980. Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's Volume I is, together with its predecessor the red book of varieties and schemes now as before, one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics! Zentralblatt MATH, 821 In the 20th century, algebraic geometry has undergone several revolutionary changes with respect to its conceptual foundations, technical framework, and intertwining with other branches of mathematics. Accordingly the way it is taught has gone through distinct phases. The theory of algebraic schemes, together with its fullblown machinery of sheaves and their cohomology, being for now the ultimate stage of this evolution process in algebraic geometry, had created  around 1960  the urgent demand for new textbooks reflecting these developments and (henceforth) various facets of algebraic geometry. ... It was David Mumford, who at first started the project of writing a textbook on algebraic geometry in its new setting. His mimeographed Harvard notes ntroduction to algebraic geometry: Preliminary version of the first three chapters (bound in red) were distributed in the mid 1960's, and they were intended as the first stage of a forthcoming, more inclusive textbook. For some years, these mimeographed notes represented the almost only, however utmost convenient and abundant source for nonexperts to get acquainted with the basic new concepts and ideas of modern algebraic geometry. Their timeless utility, in this regard, becomes apparent from the fact that two reprints of them have appeared, since 1988, as a proper book under the title he red book of varieties and schemes' ( Lect. Notes Math. 1358). In the process of exending his Harvard notes to a comprehensive textbook, the author's teaching experiences led him to the didactic conclusion that it would be better to split the book into two volumes, thereby starting with complex projective varieties (in volume I), and proceeding with schemes and their cohomology (in volume II).  In 1976, the author published the first volume under the title lgebraic geometry. I: Complex projective varieties where the corrections concerned the wiping out of some misprints, inconsistent notations, and other slight inaccuracies. The book under review is an unchanged reprint of this corrected second edition from 1980. Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's Volume I is, together with its predecessor the red book of varieties and schemes now as before, one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics! Zentralblatt MATH, 821 Author InformationBiography of David Mumford David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics. Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence. Tab Content 6Author Website:Countries AvailableAll regions 