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Complex algebraic threefolds
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ISBN: 1108946038 110893398X Year: 2024 Publisher: Cambridge ; New York, NY : Cambridge University Press,

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Abstract

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.


Book
Lectures on K3 surfaces
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ISBN: 9781107153042 1107153042 Year: 2016 Publisher: Cambridge Cambridge University Press

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Book
Lectures on K3 surfaces
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ISBN: 1316797015 1316797570 131659419X Year: 2016 Publisher: Cambridge : Cambridge University Press,

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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.


Book
Algebraic threefolds : proceedings of the 2nd 1981 session of the Centro Internazionale Matematico Estivo (CIME) held at Varenna, Italy, June 15-23, 1981
Authors: ---
ISBN: 0387115870 3540115870 3540393420 Year: 1982 Publisher: Berlin : Springer-Verl.,

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Explicit birational geometry of 3-folds
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ISBN: 1139885456 1107103487 1107092094 1107100968 1107089131 1107095344 0511758944 9781107089136 9780511758942 9781107100961 9781107095342 0521636418 9780521636414 Year: 2000 Volume: 281 Publisher: Cambridge : Cambridge University Press,

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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.

The geometry of some special arithmetic quotients
Author:
ISBN: 3540617957 354069997X 9783540617952 Year: 1996 Volume: 1637 Publisher: Berlin: Springer,


Book
Some special properties of the adjunction theory for 3-folds in P⁵
Authors: --- ---
ISSN: 00659266 ISBN: 0821802348 Year: 1995 Publisher: Providence (R.I.): American Mathematical Society


Book
Birationally rigid Fano threefold hypersurfaces
Authors: ---
ISBN: 9781470423162 Year: 2017 Publisher: Providence : American Mathematical Society,

Weyl groups and birational transformations among minimal models
Author:
ISSN: 00659266 ISBN: 0821803417 Year: 1995 Publisher: Providence (R.I.): American Mathematical Society


Book
Arithmetic and geometry of K3 surfaces and Calabi-Yau threefolds
Authors: --- --- ---
ISBN: 1489999183 1461464021 146146403X Year: 2013 Publisher: New York : Springer,

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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.

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