Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on the existence of minimal models for varieties of log general type and of the finite generation of the canonical ring. The second part is an introduction to the theory of moduli spaces. It includes topics such as representing and moduli functors, Hilbert schemes, the boundedness, local closedness and separatedness of moduli spaces and the boundedness for varieties of general type. The book is aimed at advanced graduate students and researchers in algebraic geometry.

Geometry --- landmeetkunde --- Algebraic geometry. --- Algebraic Geometry. --- Algebraic geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Algèbre commutative, Chapitres 8 et 9 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce volume du Livre d'Algèbre commutative, septième Livre du traité, comprend les chapitres : Dimension ; Anneaux locaux noethériens complets. Le chapitre 8 traite de diverses notions de dimension en algèbre commutative, telles que la dimension de Krull d'un anneau. Ces notions jouent un rôle capital en géometrie algébrique. Le chapitre 9 introduit, quant à lui, les vecteurs de Witt et les anneaux japonais. Ce volume est une réimpression de l'édition de 1983.

Ordered algebraic structures --- algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: ¢ Basic homotopy; ¢ H-spaces and co-H-spaces; ¢ Fibrations and cofibrations; ¢ Exact sequences of homotopy sets, actions, and coactions; ¢ Homotopy pushouts and pullbacks; ¢ Classical theorems, including those of Serre, Hurewicz, Blakers-Massey, and Whitehead; ¢ Homotopy sets; ¢ Homotopy and homology decompositions of spaces and maps; and ¢ Obstruction theory. The underlying theme of the entire book is the Eckmann-Hilton duality theory. This approach provides a unifying motif, clarifies many concepts, and reduces the amount of repetitious material. The subject matter is treated carefully with attention to detail, motivation is given for many results, there are several illustrations, and there are a large number of exercises of varying degrees of difficulty. It is assumed that the reader has had some exposure to the rudiments of homology theory and fundamental group theory; these topics are discussed in the appendices. The book can be used as a text for the second semester of an algebraic topology course. The intended audience of this book is advanced undergraduate or graduate students. The book could also be used by anyone with a little background in topology who wishes to learn some homotopy theory.

Algebraic topology --- topologie (wiskunde)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in n-space is as a set an intersection of (n-1) hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratýnski. The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises. Even this advanced material, presented comprehensively, keeps in mind the young student as potential reader besides the specialists of the subject.

Ordered algebraic structures --- algebra

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Algèbre commutative, Chapitres 1 à 4 Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce premier volume du Livre d'Algèbre commutative, septième Livre du traité, est consacré aux concepts fondamentaux de l'algèbre commutative. Il comprend les chapitres : Modules plats ; Localisation ; Graduations, filtrations et topologies ; Idéaux premiers associés et décomposition primaire. Il contient également des notes historiques. Ce volume est une réimpression de l'édition de 1969.

Ordered algebraic structures --- algebra