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Principles of Algebraic Geometry

Principles of Algebraic Geometry PDF Author: Phillip Griffiths
Publisher: John Wiley & Sons
ISBN: 111862632X
Category : Mathematics
Languages : en
Pages : 837

Book Description
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

Principles of Algebraic Geometry

Principles of Algebraic Geometry PDF Author: Phillip Griffiths
Publisher: John Wiley & Sons
ISBN: 111862632X
Category : Mathematics
Languages : en
Pages : 837

Book Description
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.

Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers PDF Author: Donu Arapura
Publisher: Springer Science & Business Media
ISBN: 1461418097
Category : Mathematics
Languages : en
Pages : 326

Book Description
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.

Classification Theory of Algebraic Varieties and Compact Complex Spaces

Classification Theory of Algebraic Varieties and Compact Complex Spaces PDF Author: K. Ueno
Publisher: Springer
ISBN: 3540374159
Category : Computers
Languages : en
Pages : 296

Book Description


Geometry of Higher Dimensional Algebraic Varieties

Geometry of Higher Dimensional Algebraic Varieties PDF Author: Thomas Peternell
Publisher: Birkhäuser
ISBN: 3034888937
Category : Mathematics
Languages : en
Pages : 221

Book Description
This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Algebraic Geometry I

Algebraic Geometry I PDF Author: David Mumford
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 208

Book Description
From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt

Real Algebraic Varieties

Real Algebraic Varieties PDF Author: Frédéric Mangolte
Publisher: Springer Nature
ISBN: 3030431045
Category : Mathematics
Languages : en
Pages : 453

Book Description
This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.

A Concise Introduction to Algebraic Varieties

A Concise Introduction to Algebraic Varieties PDF Author: Brian Osserman
Publisher: American Mathematical Society
ISBN: 1470466651
Category : Mathematics
Languages : en
Pages : 259

Book Description


Arithmetic of Higher-Dimensional Algebraic Varieties

Arithmetic of Higher-Dimensional Algebraic Varieties PDF Author: Bjorn Poonen
Publisher: Springer Science & Business Media
ISBN: 0817681701
Category : Mathematics
Languages : en
Pages : 292

Book Description
This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

Hodge Theory and Complex Algebraic Geometry I:

Hodge Theory and Complex Algebraic Geometry I: PDF Author: Claire Voisin
Publisher: Cambridge University Press
ISBN: 9780521718011
Category : Mathematics
Languages : en
Pages : 334

Book Description
This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Basic Algebraic Geometry 2

Basic Algebraic Geometry 2 PDF Author: Igor Rostislavovich Shafarevich
Publisher: Springer Science & Business Media
ISBN: 9783540575542
Category : Mathematics
Languages : en
Pages : 292

Book Description
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. 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 in theoretical physics.