This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on ...

This text is designed for a one-quarter or one-semester graduate couse in Riemannian geometry. It focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics, and then introduces the Riemann ...

In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, ...

Dieses Buch ist aus einer Reihe von Vorlesungen an der Universität Bonn entstanden, die sich an Studierende im Hauptstudium wandte. Es beginnt mit einer Einführung in die homologische Algebra, die Garbentheorie und die Kohomologie von Garben. Darauf aufbauend kommt eine Einführung in die moderne algebraische Geometrie. ...

Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometriezusammen mit einer Reihe von Beispielen darzustellen. Dies soll es dem Leser ermöglichen, selbstständig mit weiterführenden Texten zu arbeiten. Die Sprache wird bewusst elementar gehalten, so werden Garben- und Kohomologietheorie in diesem Buch nicht behandelt. Besonderes Gewicht wird auf die Darstellung ...

Beginnend mit der Fragestellung nach zuverlässiger Datenübertragung wird die elementare lineare Codierungstheorie dargestellt. insbesondere wird das Problem der Konstruktion von optimalen Codes herausgearbeitet. Dieses anspruchsvolle Problem wird mit allen Mitteln der algebraischen Geometrie gelöst. Das Buch liefert einen schnellen elementaren Zugang zu den algebraischen Kurven und führt den Leser an die grundlegenden ...

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures ...

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier generations of number theorists. This integration has led to proofs of some of the major conjectures ...

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of ...

This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and ...