Ernst Kunz – författare

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the reader only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. Examples, exercises, figures, and suggestions for further study round out this fairly self-contained textbook.

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the reader only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed. Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. Examples, exercises, figures, and suggestions for further study round out this fairly self-contained textbook.

Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Dieses Buch kann als Fortsetzung der "Algebra" desselben Autors angesehen werden. Es handelt von algebraischen Varietäten im affinen und projektiven Raum, das sind die Lösungsmengen von Systemen algebraischer Gleichungen. Im Mittelpunkt stehen die grundlegenden Begriffe, wie reguläre und rationale Funktionen, Dimensionen, Singularitäten und deren Eigenschaften. Darüber hinaus wird zum Konzept des Schemas hingeführt und dessen Nutzen in der Schnitt-Theorie gezeigt. An algebraischen Hilfsmitteln wird nur das verwendet, was zu einer einführenden Vorlesung gehört. Weitergehende Techniken der kommutativen Algebra sind in einem Anhang bereitgestellt. Außerdem können Abbildungen und Übungsaufgaben dem Leser helfen, sich mit diesem besonders faszinierenden Teil der Geometrie anzufreunden.