The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations.
Content and Subject Matter: This research monograph deals with two main subjects, namely the notion of equimultiplicity and the algebraic study of various graded rings in relation to blowing ups.
The first edition of this book came out just as the apparatus of algebraic geometry was reaching a stage that permitted a lucid and concise account of the foundations of the subject.
This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors.
The present volume contains, together with numerous additions and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the Centro Internazionale Mate- matico Estivo .
This is the sixth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research.
The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus.
The main goal of the CIME Summer School on "e;Algebraic Cycles and Hodge Theory"e; has been to gather the most active mathematicians in this area to make the point on the present state of the art.
This volume of research papers is an outgrowth of the Manin Seminar at Moscow University, devoted to K-theory, homological algebra and algebraic geometry.
In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry.
It is well known that there are close relations between classes of singularities and representation theory via the McKay correspondence and between representation theory and vector bundles on projective spaces via the Bernstein-Gelfand-Gelfand construction.
The study of hypersurface quadrilateral singularities can bereduced to the study of elliptic K3 surfaces with a singularfiber of type I * 0 (superscript *, subscript 0), andtherefore these notes consider, besides the topics of thetitle, such K3 surfaces too.
In the Teichmuller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years.
