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The first book on the explicit birational geometry of complex algebraic threefolds arising from the minimal model program, this text is sure to become an essential reference in the field of birational geometry. Threefolds remain the interface between low and high-dimensional settings and a good understanding of them is necessary in this actively evolving area. Intended for advanced graduate students as well as researchers working in birational geometry, the book is as self-contained as possible. Detailed proofs are given throughout and more than 100 examples help to deepen understanding of birational geometry. The first part of the book deals with threefold singularities, divisorial contractions and flips. After a thorough explanation of the Sarkisov program, the second part is devoted to the analysis of outputs, specifically minimal models and Mori fibre spaces. The latter are divided into conical fibrations, del Pezzo fibrations and Fano threefolds according to the relative dimension.
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Surfaces, Algebraic --- Threefolds (Algebraic geometry) --- Geometry, Algebraic
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K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
Surfaces, Algebraic. --- Threefolds (Algebraic geometry) --- Geometry, Algebraic.
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Solids --- Threefolds (Algebraic geometry) --- Data processing. --- Mathematical models. --- Congresses. --- Algebraic geometry --- Géométrie algébrique --- Mathématiques
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One of the main achievements of algebraic geometry over the last 30 years is the work of Mori and others extending minimal models and the Enriques-Kodaira classification to 3-folds. This book, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper Corti, Pukhlikov and Reid) work out in detail the theory of birational rigidity of Fano 3-folds; these contributions work for the first time with a representative class of Fano varieties, 3-fold hypersurfaces in weighted projective space, and include an attractive introductory treatment and a wealth of detailed computation of special cases.
Threefolds (Algebraic geometry) --- Geometry, Algebraic. --- Surfaces, Algebraic. --- Algebraic surfaces --- Geometry, Algebraic --- Algebraic geometry --- Geometry --- 3-folds (Algebraic geometry) --- Three-folds (Algebraic geometry) --- Algebraic varieties
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Group theory --- Algebraic geometry --- 3-folds (Algebraic geometry) --- Coefficiententheorie --- Drievouden (Algebraïsche geometrie) --- Moduli theory --- Oppervlakken [Algebraïsche ] --- Surfaces [Algebraic ] --- Surfaces algébriques --- Theorie des coefficients --- Three-folds (Algebraic geometry) --- Threefolds (Algebraic geometry) --- Variétés à 3 dimensions --- Moduli theory. --- Surfaces, Algebraic. --- Threefolds(Algebraic geometry) --- Surfaces, algebraic
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Hypersurfaces. --- Threefolds (Algebraic geometry) --- Surfaces, Algebraic. --- Rigidity (Geometry) --- Hypersurfaces --- Variétés à 3 dimensions --- Surfaces algebriques --- Rigidité (Géométrie) --- Surfaces, Algebraic --- Surfaces algébriques --- Rigidité (géométrie) --- Variétés à 3 dimensions --- Rigidité (Géométrie) --- Variétés à 3 dimensions. --- Surfaces algébriques.
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Topological groups. Lie groups --- Algebraic geometry --- Surfaces, Algebraic --- Weyl groups --- Threefolds (Algebraic geometry) --- Surfaces algébriques. --- Groupes de Weyl. --- Variétés à 3 dimensions. --- Weyl's groups --- Group theory --- 3-folds (Algebraic geometry) --- Three-folds (Algebraic geometry) --- Algebraic varieties --- Geometry, Algebraic --- Algebraic surfaces
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In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on Arithmetic and Geometry of K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16–25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the large variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.
Manifolds (Mathematics). --- Surfaces. --- Threefolds (Algebraic geometry) --- Surfaces, Algebraic --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Manifolds (Mathematics) --- Curved surfaces --- Mathematics. --- Algebraic geometry. --- Differential geometry. --- Number theory. --- Mathematical physics. --- Algebraic Geometry. --- Number Theory. --- Differential Geometry. --- Mathematical Physics. --- Geometry, Differential --- Topology --- Shapes --- Geometry, algebraic. --- Global differential geometry. --- Algebraic geometry --- Number study --- Numbers, Theory of --- Algebra --- Physical mathematics --- Physics --- Differential geometry
Listing 1 - 10 of 11 | << page >> |
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