## Lectures On Algebraic Geometry Ii

**Author**: Günter Harder

**Editor:**Springer Science & Business Media

**ISBN:**3834881597

**File Size**: 51,20 MB

**Format:**PDF

**Read:**1979

This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.

## Lectures On Algebraic Geometry I

**Author**: Günter Harder

**Editor:**Springer Science & Business Media

**ISBN:**3834883301

**File Size**: 51,81 MB

**Format:**PDF, Docs

**Read:**238

This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them. For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II.

## Algebraic Geometry

**Author**:

**Editor:**

**ISBN:**

**File Size**: 36,91 MB

**Format:**PDF, ePub, Docs

**Read:**4351

## Lectures On Algebra

**Author**: Shreeram Shankar Abhyankar

**Editor:**World Scientific

**ISBN:**9812568263

**File Size**: 30,11 MB

**Format:**PDF, ePub, Docs

**Read:**4422

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

## Algebraic Geometry Ii

**Author**: I.R. Shafarevich

**Editor:**Springer Science & Business Media

**ISBN:**9783540546801

**File Size**: 58,44 MB

**Format:**PDF, Mobi

**Read:**8358

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

## Arithmetic Algebraic Geometry

**Author**: Jean-Louis Colliot-Thelene

**Editor:**Springer

**ISBN:**3540479090

**File Size**: 42,10 MB

**Format:**PDF, Mobi

**Read:**1659

This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

## The Red Book Of Varieties And Schemes

**Author**: David Mumford

**Editor:**Springer

**ISBN:**3540460217

**File Size**: 28,92 MB

**Format:**PDF, ePub, Mobi

**Read:**5331

Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.

## Lectures On Algebraic Topology

**Author**: Sergeĭ Vladimirovich Matveev

**Editor:**European Mathematical Society

**ISBN:**9783037190234

**File Size**: 68,64 MB

**Format:**PDF

**Read:**4264

Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

## Algebraic Geometry

**Author**: Joe Harris

**Editor:**Springer Science & Business Media

**ISBN:**1475721897

**File Size**: 22,61 MB

**Format:**PDF

**Read:**823

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

## Lectures On Curves On An Algebraic Surface

**Author**: David Mumford

**Editor:**Princeton University Press

**ISBN:**9780691079936

**File Size**: 36,33 MB

**Format:**PDF, Docs

**Read:**4857

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.

## Lectures On Formal And Rigid Geometry

**Author**: Siegfried Bosch

**Editor:**Springer

**ISBN:**3319044176

**File Size**: 79,38 MB

**Format:**PDF, ePub

**Read:**2637

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".

## Lectures In Algebraic Geometry

**Author**: Shreeram Shankar Abhyankar

**Editor:**

**ISBN:**

**File Size**: 77,39 MB

**Format:**PDF, ePub

**Read:**9631

## Contributions To Algebraic Geometry

**Author**: Piotr Pragacz

**Editor:**European Mathematical Society

**ISBN:**9783037191149

**File Size**: 15,66 MB

**Format:**PDF, ePub, Mobi

**Read:**9204

The articles in this volume cover a broad range of topics in algebraic geometry: classical varieties, linear system, birational geometry, Minimal Model Program, moduli spaces, toric varieties, enumerative theory of singularities, equivariant cohomology and arithmetic questions.

## Lectures By S Lefschetz On Algebraic Geometry 1936 1938

**Author**: Solomon Lefschetz

**Editor:**

**ISBN:**

**File Size**: 41,39 MB

**Format:**PDF, ePub

**Read:**9428

## Hodge Theory And Complex Algebraic Geometry Ii Volume 2

**Author**: Claire Voisin

**Editor:**Cambridge University Press

**ISBN:**9781139437707

**File Size**: 57,77 MB

**Format:**PDF

**Read:**9282

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard–Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether–Lefschetz theorems, the generic triviality of the Abel–Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.

## Geometry Ii

**Author**: Marcel Berger

**Editor:**Springer Science & Business Media

**ISBN:**3540938168

**File Size**: 45,33 MB

**Format:**PDF, Mobi

**Read:**1446

This is the second of a two-volume textbook that provides a very readable and lively presentation of large parts of geometry in the classical sense. For each topic the author presents a theorem that is esthetically pleasing and easily stated, although the proof may be quite hard and concealed. Yet another strong trait of the book is that it provides a comprehensive and unified reference source for the field of geometry in the full breadth of its subfields and ramifications.

## Introduction To Algebraic Geometry And Commutative Algebra

**Author**: Dilip P. Patil

**Editor:**World Scientific

**ISBN:**9814304573

**File Size**: 30,42 MB

**Format:**PDF, ePub, Mobi

**Read:**4734

Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.

## Algebraic Geometry

**Author**: Robin Hartshorne

**Editor:**Springer Science & Business Media

**ISBN:**1475738498

**File Size**: 46,63 MB

**Format:**PDF

**Read:**3431

An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

## An Invitation To Noncommutative Geometry

**Author**: Masoud Khalkhali

**Editor:**World Scientific

**ISBN:**9812814337

**File Size**: 53,88 MB

**Format:**PDF, Kindle

**Read:**351

A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo

## Lectures On Invariant Theory

**Author**: Igor Dolgachev

**Editor:**Cambridge University Press

**ISBN:**9780521525480

**File Size**: 30,28 MB

**Format:**PDF, Docs

**Read:**9561

Table of contents