Complex Algebraic Varieties

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Classification Theory Of Algebraic Varieties And Compact Complex Spaces

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Author : K. Ueno
language : en
Publisher: Springer
Release Date : 2006-11-15

Classification Theory Of Algebraic Varieties And Compact Complex Spaces written by K. Ueno and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Computers categories.

Real Algebraic Varieties

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Author : Frédéric Mangolte
language : en
Publisher: Springer Nature
Release Date : 2020-09-21

Real Algebraic Varieties written by Frédéric Mangolte and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.

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.

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.

Arithmetic Of Higher Dimensional Algebraic Varieties

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Author : Bjorn Poonen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Arithmetic Of Higher Dimensional Algebraic Varieties written by Bjorn Poonen 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 2012-12-06 with Mathematics categories.

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. This text, which focuses on higher dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry.

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.

Hodge Theory And Complex Algebraic Geometry I

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Author : Claire Voisin
language : en
Publisher: Cambridge University Press
Release Date : 2007-12-20

Hodge Theory And Complex Algebraic Geometry I written by Claire Voisin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-20 with Mathematics categories.

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.

Complex Algebraic Geometry

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Author : János Kollár
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Complex Algebraic Geometry written by János Kollár 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 1997 with Mathematics categories.

Lecture notes from the Third Summer Session of the Regional Geometry Institute, held in Park City, Utah, in 1993.

Algebraic Geometry I

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Author : V.I. Danilov
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-17

Algebraic Geometry I written by V.I. Danilov 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 1998-03-17 with Mathematics categories.

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Principles Of Algebraic Geometry

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Author : Phillip Griffiths
language : en
Publisher: John Wiley & Sons
Release Date : 2014-08-21

Principles Of Algebraic Geometry written by Phillip Griffiths and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-21 with Mathematics categories.

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.

Complex Algebraic Curves

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Author : Frances Clare Kirwan
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-20

Complex Algebraic Curves written by Frances Clare Kirwan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-20 with Mathematics categories.

This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.