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The Poincare Conjecture: In Search of the Shape of the Universe
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Donal O'Shea
In telling this vibrant story, O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians.
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Algebraic Surfaces
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Oscar Zariski
Presents the methods of classical algebraic geometry.
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Resolution of Singularities of Embedded Algebraic Surfaces
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Shreeram S Abhyankar
This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization ...
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Degeneration of Abelian Varieties
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Gerd Faltings
This book presents a complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space. Most results are new and have never been published before. Highlights of the book include a classification of semi-abelian schemes, construction of the ...
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Algebraic Surfaces
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Lucian Badescu, Vladimir Masek
This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is ...
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Algebraic Surfaces and Holomorphic Vector Bundles
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Robert Friedman
This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, ...
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Complex Algebraic Surfaces
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Beauville
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern ...
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Surface topology
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P A Firby
This text examines the topology of compact surfaces through the development of some simple ideas in place geometry, an approach which allows a treatment of an area of mathematics that is particularly attractive both for the richness of its applications, and for the variety of its interactions with other branches of mathematics. A wide variety of ...
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Geometry and Interpolation of Curves and Surfaces
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Robin J Y McLeod, M Louisa Baart
This text takes a practical, step-by-step approach to algebraic curves and surface interpolation motivated by the understanding of the many practical applications in engineering analysis, approximation, and curve plotting problems. Because of its usefulness for computing, the algebraic approach is the main theme, but a brief discussion of the ...
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Smooth Four-Manifolds and Complex Surfaces
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by
Robert Friedman
This book applies the recent techniques of gauge theory to study the smooth classification of compact complex surfaces. The study is divided into four main areas: Classical complex surface theory, gauge theory and Donaldson invariants, deformations of holomorphic vector bundles, and explicit calculations for elliptic sur faces. The book represents ...
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Complex surfaces and connected sums of complex projective planes
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B Moishezon
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Birational Geometry of Algebraic Varieties
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Janos Kollar, Shigefumi Mori
One of the major discoveries of the last two decades of the twentieth century in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program or Mori's program, has developed into a powerful tool with applications to ...
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Compact Complex Surfaces
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Wolf Barth
The first edition of "Compact Complex Surfaces" was published in 1984 and has become one of the most important books on the subject. In this second enlarged edition the major developments of the last 20 years have been incorporated. The Enriques-Kodaira classification is carried out in the spirit of Mori theory and many new developments have been ...
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An Introduction to the Theory of Algebraic Surfaces
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Oscar Zariski
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Resolution of Curve and Surface Singularities: In Characteristic Zero
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K Kiyek, J L Vicente
This book covers the beautiful theory of resolutions of surface singularities in characteristic zero. The primary goal is to present in detail, and for the first time in one volume, two proofs for the existence of such resolutions. One construction was introduced by H.W.E. Jung, and another is due to O. Zariski. Jung's approach uses quasi-ordinary ...
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Holomorphic Vector Bundles Over Compact Complex Surfaces
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Vasile Brinzanescu
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector ...
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Monomialization of Morphisms from 3-Folds to Surfaces
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Steven Dale Cutkosky
A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. ...
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Non-Complete Algebraic Surfaces
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Masayoshi Miyanishi
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The Geometry of Some Special Arithmetic Quotients
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by
Bruce Hunt
The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest ...
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Lectures on curves on an algebraic surface.
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David Mumford
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Lmsst: 34 Complex Algebraic Surfaces 2ed
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by
Arnaud Beauville
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern ...
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K3 Projective Models in Scrolls
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Trygve Johnsen, Andreas L Knutsen
The exposition studies projective models of K3 surfaces whose hyperplane sections are non-Clifford general curves. These models are contained in rational normal scrolls. The exposition supplements standard descriptions of models of general K3 surfaces in projective spaces of low dimension, and leads to a classification of K3 surfaces in projective ...
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Resolution of Surface Singularities
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Vincent Cossart, Jean Giraud, Ulrich Orbanz
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Hodge Theory and the Local Torelli Problem
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Loring W. Tu
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Surfaces Algebriques
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J Giraud
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