Lectures On Resolution Of Singularities Am 166

Author : János Kollár
Publisher : Princeton University Press
ISBN 13 : 1400827809
Total Pages : 215 pages
Book Rating : 4.00/5 ( download)

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Download or read book Lectures on Resolution of Singularities (AM-166) written by János Kollár and published by Princeton University Press. This book was released on 2009-01-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resolution of singularities is a powerful and frequently used tool in algebraic geometry. In this book, János Kollár provides a comprehensive treatment of the characteristic 0 case. He describes more than a dozen proofs for curves, many based on the original papers of Newton, Riemann, and Noether. Kollár goes back to the original sources and presents them in a modern context. He addresses three methods for surfaces, and gives a self-contained and entirely elementary proof of a strong and functorial resolution in all dimensions. Based on a series of lectures at Princeton University and written in an informal yet lucid style, this book is aimed at readers who are interested in both the historical roots of the modern methods and in a simple and transparent proof of this important theorem.

Author : János Kollár
Publisher :
ISBN 13 : 9780691129228
Total Pages : 208 pages
Book Rating : 4.23/5 ( download)

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Download or read book Annals of Mathematics Studies written by János Kollár and published by . This book was released on 1940 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Andrei Verona
Publisher :
ISBN 13 : 9780387139043
Total Pages : 238 pages
Book Rating : 4.44/5 ( download)

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Download or read book Resolution of Surface Singularities written by Andrei Verona and published by . This book was released on 1984 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Andreas Hochenegger
Publisher : Springer Nature
ISBN 13 : 3030186385
Total Pages : 297 pages
Book Rating : 4.88/5 ( download)

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Download or read book Birational Geometry of Hypersurfaces written by Andreas Hochenegger and published by Springer Nature. This book was released on 2019-10-08 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Author : Antoine Chambert-Loir
Publisher : Springer
ISBN 13 : 149397887X
Total Pages : 526 pages
Book Rating : 4.78/5 ( download)

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Download or read book Motivic Integration written by Antoine Chambert-Loir and published by Springer. This book was released on 2018-09-15 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since.

Author : Paolo Cascini
Publisher : Springer
ISBN 13 : 3319244604
Total Pages : 216 pages
Book Rating : 4.00/5 ( download)

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Download or read book Foliation Theory in Algebraic Geometry written by Paolo Cascini and published by Springer. This book was released on 2016-03-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring a blend of original research papers and comprehensive surveys from an international team of leading researchers in the thriving fields of foliation theory, holomorphic foliations, and birational geometry, this book presents the proceedings of the conference "Foliation Theory in Algebraic Geometry," hosted by the Simons Foundation in New York City in September 2013. Topics covered include: Fano and del Pezzo foliations; the cone theorem and rank one foliations; the structure of symmetric differentials on a smooth complex surface and a local structure theorem for closed symmetric differentials of rank two; an overview of lifting symmetric differentials from varieties with canonical singularities and the applications to the classification of AT bundles on singular varieties; an overview of the powerful theory of the variety of minimal rational tangents introduced by Hwang and Mok; recent examples of varieties which are hyperbolic and yet the Green-Griffiths locus is the whole of X; and a classification of psuedoeffective codimension one distributions. Foliations play a fundamental role in algebraic geometry, for example in the proof of abundance for threefolds and to a solution of the Green-Griffiths conjecture for surfaces of general type with positive Segre class. The purpose of this volume is to foster communication and enable interactions between experts who work on holomorphic foliations and birational geometry, and to bring together leading researchers to demonstrate the powerful connection of ideas, methods, and goals shared by these two areas of study./div

Author : Jean-Pierre Serre
Publisher : CRC Press
ISBN 13 : 1466501936
Total Pages : 174 pages
Book Rating : 4.35/5 ( download)

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Download or read book Lectures on N_X(p) written by Jean-Pierre Serre and published by CRC Press. This book was released on 2016-04-19 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic cohomology and group representations, presented in a context that is appealing to specialists in number theory and algebraic geometry. Along with covering open problems, the text examines the size and congruence properties of NX(p) and describes the ways in which it is computed, by closed formulae and/or using efficient computers. The first four chapters cover the preliminaries and contain almost no proofs. After an overview of the main theorems on NX(p), the book offers simple, illustrative examples and discusses the Chebotarev density theorem, which is essential in studying frobenian functions and frobenian sets. It also reviews l-adic cohomology. The author goes on to present results on group representations that are often difficult to find in the literature, such as the technique of computing Haar measures in a compact l-adic group by performing a similar computation in a real compact Lie group. These results are then used to discuss the possible relations between two different families of equations X and Y. The author also describes the Archimedean properties of NX(p), a topic on which much less is known than in the l-adic case. Following a chapter on the Sato-Tate conjecture and its concrete aspects, the book concludes with an account of the prime number theorem and the Chebotarev density theorem in higher dimensions.

Author : Vincent Cossart
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.21/5 ( download)

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Download or read book Resolution of Surface Singularities written by Vincent Cossart and published by . This book was released on 1984 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Denis Ch‚niot
Publisher : World Scientific
ISBN 13 : 9812704108
Total Pages : 1083 pages
Book Rating : 4.08/5 ( download)

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Download or read book Singularity Theory written by Denis Ch‚niot and published by World Scientific. This book was released on 2007 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.

Author : Jean-paul Brasselet
Publisher : World Scientific
ISBN 13 : 9814476390
Total Pages : 1083 pages
Book Rating : 4.93/5 ( download)

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Download or read book Singularity Theory: Dedicated To Jean-paul Brasselet On His 60th Birthday - Proceedings Of The 2005 Marseille Singularity School And Conference written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-02-08 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Singularity School and Conference took place in Luminy, Marseille, from January 24th to February 25th 2005. More than 180 mathematicians from over 30 countries converged to discuss recent developments in singularity theory.The volume contains the elementary and advanced courses conducted by singularities specialists during the conference, general lectures on singularity theory, and lectures on applications of the theory to various domains. The subjects range from geometry and topology of singularities, through real and complex singularities, to applications of singularities.