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Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Book Synopsis Classification of Higher Dimensional Algebraic Varieties by : Christopher D. Hacon
Download or read book Classification of Higher Dimensional Algebraic Varieties written by Christopher D. Hacon and published by Springer Science & Business Media. This book was released on 2011-02-02 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Book Synopsis Classification of Higher Dimensional Algebraic Varieties by : Christopher D. Hacon
Download or read book Classification of Higher Dimensional Algebraic Varieties written by Christopher D. Hacon and published by Springer Science & Business Media. This book was released on 2010-05-27 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of algebraic varieties, toric varieties. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of areas of current research.
Book Synopsis Classification of Algebraic Varieties by : Ciro Ciliberto
Download or read book Classification of Algebraic Varieties written by Ciro Ciliberto and published by American Mathematical Soc.. This book was released on 1994 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Algebraic Geometry Conference on Classification of Algebraic Varieties, held in May 1992 at the University of L'Aquila in Italy. The papers discuss a wide variety of problems that illustrate interactions between algebraic geometry and other branches of mathematics. Among the topics covered are algebraic curve theory, algebraic surface theory, the theory of minimal models, braid groups and the topology of algebraic varieties, toric varieties. In addition to algebraic geometers, theoretical physicists in some areas will find this book useful. The book is also suitable for an advanced graduate course in algebraic geometry, as it provides an overview of areas of current research.
Book Synopsis Classification Theory of Algebraic Varieties and Compact Complex Spaces by : K. Ueno
Download or read book Classification Theory of Algebraic Varieties and Compact Complex Spaces written by K. Ueno and published by Springer. This book was released on 2006-11-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Algebraic geometry has always been an ec1ectic science, with its roots in algebra, function-theory and topology. Apart from early resear ches, now about a century old, this beautiful branch of mathematics has for many years been investigated chiefly by the Italian school which, by its pioneer work, based on algebro-geometric methods, has succeeded in building up an imposing body of knowledge. Quite apart from its intrinsic interest, this possesses high heuristic value since it represents an essential step towards the modern achievements. A certain lack of rigour in the c1assical methods, especially with regard to the foundations, is largely justified by the creative impulse revealed in the first stages of our subject; the same phenomenon can be observed, to a greater or less extent, in the historical development of any other science, mathematical or non-mathematical. In any case, within the c1assical domain itself, the foundations were later explored and consolidated, principally by SEVERI, on lines which have frequently inspired further investigations in the abstract field. About twenty-five years ago B. L. VAN DER WAERDEN and, later, O. ZARISKI and A. WEIL, together with their schools, established the methods of modern abstract algebraic geometry which, rejecting the c1assical restriction to the complex groundfield, gave up geometrical intuition and undertook arithmetisation under the growing influence of abstract algebra.
Book Synopsis Algebraic Varieties by : M. Baldassarri
Download or read book Algebraic Varieties written by M. Baldassarri and published by Springer. This book was released on 2012-07-21 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry has always been an ec1ectic science, with its roots in algebra, function-theory and topology. Apart from early resear ches, now about a century old, this beautiful branch of mathematics has for many years been investigated chiefly by the Italian school which, by its pioneer work, based on algebro-geometric methods, has succeeded in building up an imposing body of knowledge. Quite apart from its intrinsic interest, this possesses high heuristic value since it represents an essential step towards the modern achievements. A certain lack of rigour in the c1assical methods, especially with regard to the foundations, is largely justified by the creative impulse revealed in the first stages of our subject; the same phenomenon can be observed, to a greater or less extent, in the historical development of any other science, mathematical or non-mathematical. In any case, within the c1assical domain itself, the foundations were later explored and consolidated, principally by SEVERI, on lines which have frequently inspired further investigations in the abstract field. About twenty-five years ago B. L. VAN DER WAERDEN and, later, O. ZARISKI and A. WEIL, together with their schools, established the methods of modern abstract algebraic geometry which, rejecting the c1assical restriction to the complex groundfield, gave up geometrical intuition and undertook arithmetisation under the growing influence of abstract algebra.
Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.
Book Synopsis Classification of Algebraic Varieties by : Carel Faber
Download or read book Classification of Algebraic Varieties written by Carel Faber and published by European Mathematical Society. This book was released on 2011 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fascinating and surprising developments are taking place in the classification of algebraic varieties. The work of Hacon and McKernan and many others is causing a wave of breakthroughs in the minimal model program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony to the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.
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.
Book Synopsis Geometry of Higher Dimensional Algebraic Varieties by : Thomas Peternell
Download or read book Geometry of Higher Dimensional Algebraic Varieties written by Thomas Peternell and published by Birkhäuser. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classification of Algebraic Varieties and Compact Complex Manifolds by : H. Popp
Download or read book Classification of Algebraic Varieties and Compact Complex Manifolds written by H. Popp and published by Springer. This book was released on 2006-11-15 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Book Synopsis Representations of Fundamental Groups of Algebraic Varieties by : Kang Zuo
Download or read book Representations of Fundamental Groups of Algebraic Varieties written by Kang Zuo and published by Springer Science & Business Media. This book was released on 1999-12-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
Book Synopsis Moduli Theory and Classification Theory of Algebraic Varieties by : H. Popp
Download or read book Moduli Theory and Classification Theory of Algebraic Varieties written by H. Popp and published by Springer. This book was released on 2006-11-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
