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Basic Algebraic Geometry 2

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Basic Algebraic Geometry 2

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Author : Igor R. Shafarevich
language : en
Publisher: Springer
Release Date : 2012-11-27

Basic Algebraic Geometry 2 written by Igor R. Shafarevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-27 with Mathematics categories.

The second volume of Shafarevich's introductory book on algebraic varieties and complex manifolds. As with Volume 1, the author has revised the text and added new material, e.g. as a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum, making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as those in theoretical physics.

Algebraic Geometry Ii

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Author : I.R. Shafarevich
language : en
Publisher: Springer
Release Date : 2014-10-05

Algebraic Geometry Ii written by I.R. Shafarevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-05 with Mathematics categories.

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.

Positivity In Algebraic Geometry I

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Author : R.K. Lazarsfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-08-24

Positivity In Algebraic Geometry I written by R.K. Lazarsfeld and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-24 with History categories.

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.

Algebraic Geometry 2

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Author : Kenji Ueno
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Algebraic Geometry 2 written by Kenji Ueno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Modern algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in ""Algebraic Geometry 1: From Algebraic Varieties to Schemes"", (see Volume 185 in the same series, ""Translations of Mathematical Monographs""). In the present book, Ueno turns to the theory of sheaves and their cohomology. Loosely speaking, a sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.The primary tool in understanding sheaves is cohomology. For example, in studying ampleness, it is frequently useful to translate a property of sheaves into a statement about its cohomology. The text covers the important topics of sheaf theory, including types of sheaves and the fundamental operations on them, such as...coherent and quasicoherent sheaves. proper and projective morphisms. direct and inverse images. Cech cohomology. For the mathematician unfamiliar with the language of schemes and sheaves, algebraic geometry can seem distant.However, Ueno makes the topic seem natural through his concise style and his insightful explanations. He explains why things are done this way and supplements his explanations with illuminating examples. As a result, he is able to make algebraic geometry very accessible to a wide audience of non-specialists. The book contains numerous problems and exercises with solutions. It would be an excellent text for the second part of a course in algebraic geometry.

Lectures On Algebraic Geometry Ii

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Author : Günter Harder
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-21

Lectures On Algebraic Geometry Ii written by Günter Harder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-21 with Mathematics categories.

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.

An Invitation To Algebraic Geometry

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Author : Karen E. Smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

An Invitation To Algebraic Geometry written by Karen E. Smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Basic Algebraic Geometry 2

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Author : Igor R. Shafarevich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-31

Basic Algebraic Geometry 2 written by Igor R. Shafarevich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-31 with Mathematics categories.

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

Basic Algebraic Geometry 2

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Author : Igor R. Shafarevich
language : en
Publisher: Springer
Release Date : 2013-09-10

Algebraic Geometry

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Author : Robin Hartshorne
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Algebraic Geometry written by Robin Hartshorne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

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 Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.

Algebraic Geometry Over The Complex Numbers

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Author : Donu Arapura
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-15

Algebraic Geometry Over The Complex Numbers written by Donu Arapura and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-15 with Mathematics categories.

This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.

Basic Algebraic Geometry 2

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