Mixed Hodge Structures and Singularities

Download Mixed Hodge Structures and Singularities PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521620604
Total Pages : 210 pages
Book Rating : 4.6/5 (26 download)

DOWNLOAD NOW!


Book Synopsis Mixed Hodge Structures and Singularities by : Valentine S. Kulikov

Download or read book Mixed Hodge Structures and Singularities written by Valentine S. Kulikov and published by Cambridge University Press. This book was released on 1998-04-27 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This vital work is both an introduction to, and a survey of singularity theory, in particular, studying singularities by means of differential forms. Here, some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss-Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This is an excellent resource for all researchers in singularity theory, algebraic or differential geometry.

Mixed Hodge Structures

Download Mixed Hodge Structures PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9783540770176
Total Pages : 470 pages
Book Rating : 4.7/5 (71 download)

DOWNLOAD NOW!


Book Synopsis Mixed Hodge Structures by : Chris A.M. Peters

Download or read book Mixed Hodge Structures written by Chris A.M. Peters and published by Springer Science & Business Media. This book was released on 2008-02-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is comprehensive basic monograph on mixed Hodge structures. Building up from basic Hodge theory the book explains Delingne's mixed Hodge theory in a detailed fashion. Then both Hain's and Morgan's approaches to mixed Hodge theory related to homotopy theory are sketched. Next comes the relative theory, and then the all encompassing theory of mixed Hodge modules. The book is interlaced with chapters containing applications. Three large appendices complete the book.

Period Mappings and Period Domains

Download Period Mappings and Period Domains PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 1108422624
Total Pages : 577 pages
Book Rating : 4.1/5 (84 download)

DOWNLOAD NOW!


Book Synopsis Period Mappings and Period Domains by : James Carlson

Download or read book Period Mappings and Period Domains written by James Carlson and published by Cambridge University Press. This book was released on 2017-08-24 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Intersection Homology & Perverse Sheaves

Download Intersection Homology & Perverse Sheaves PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030276449
Total Pages : 270 pages
Book Rating : 4.0/5 (32 download)

DOWNLOAD NOW!


Book Synopsis Intersection Homology & Perverse Sheaves by : Laurenţiu G. Maxim

Download or read book Intersection Homology & Perverse Sheaves written by Laurenţiu G. Maxim and published by Springer Nature. This book was released on 2019-11-30 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Hodge Theory (MN-49)

Download Hodge Theory (MN-49) PDF Online Free

Author :
Publisher : Princeton University Press
ISBN 13 : 1400851475
Total Pages : 608 pages
Book Rating : 4.4/5 (8 download)

DOWNLOAD NOW!


Book Synopsis Hodge Theory (MN-49) by : Eduardo Cattani

Download or read book Hodge Theory (MN-49) written by Eduardo Cattani and published by Princeton University Press. This book was released on 2014-07-21 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.

Singularities

Download Singularities PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821814664
Total Pages : 680 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!


Book Synopsis Singularities by : Peter Orlik

Download or read book Singularities written by Peter Orlik and published by American Mathematical Soc.. This book was released on 1983 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This work presents the written versions of all but three of the invited talks presented at this Symposium. It contains 2 papers by invited speakers who aren't able to attend.

Recent Advances in Hodge Theory

Download Recent Advances in Hodge Theory PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 110754629X
Total Pages : 533 pages
Book Rating : 4.1/5 (75 download)

DOWNLOAD NOW!


Book Synopsis Recent Advances in Hodge Theory by : Matt Kerr

Download or read book Recent Advances in Hodge Theory written by Matt Kerr and published by Cambridge University Press. This book was released on 2016-02-04 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Trends in Singularities

Download Trends in Singularities PDF Online Free

Author :
Publisher : Birkhäuser
ISBN 13 : 3034881614
Total Pages : 250 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!


Book Synopsis Trends in Singularities by : Anatoly Libgober

Download or read book Trends in Singularities written by Anatoly Libgober and published by Birkhäuser. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection of papers in this volume represents recent advances in the under standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

Handbook of Geometry and Topology of Singularities III

Download Handbook of Geometry and Topology of Singularities III PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030957608
Total Pages : 822 pages
Book Rating : 4.0/5 (39 download)

DOWNLOAD NOW!


Book Synopsis Handbook of Geometry and Topology of Singularities III by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Introduction to Singularities

Download Introduction to Singularities PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 4431568379
Total Pages : 236 pages
Book Rating : 4.4/5 (315 download)

DOWNLOAD NOW!


Book Synopsis Introduction to Singularities by : Shihoko Ishii

Download or read book Introduction to Singularities written by Shihoko Ishii and published by Springer. This book was released on 2018-09-21 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.

Singularities of Differentiable Maps, Volume 2

Download Singularities of Differentiable Maps, Volume 2 PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0817683437
Total Pages : 492 pages
Book Rating : 4.8/5 (176 download)

DOWNLOAD NOW!


Book Synopsis Singularities of Differentiable Maps, Volume 2 by : Elionora Arnold

Download or read book Singularities of Differentiable Maps, Volume 2 written by Elionora Arnold and published by Springer Science & Business Media. This book was released on 2012-05-16 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​​​The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originally published as Volume 82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of the anatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how they function.

Singularities of Caustics and Wave Fronts

Download Singularities of Caustics and Wave Fronts PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 9401133301
Total Pages : 271 pages
Book Rating : 4.4/5 (11 download)

DOWNLOAD NOW!


Book Synopsis Singularities of Caustics and Wave Fronts by : Vladimir Arnold

Download or read book Singularities of Caustics and Wave Fronts written by Vladimir Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Motivic Aspects of Hodge Theory

Download Motivic Aspects of Hodge Theory PDF Online Free

Author :
Publisher :
ISBN 13 : 9788184870121
Total Pages : 0 pages
Book Rating : 4.8/5 (71 download)

DOWNLOAD NOW!


Book Synopsis Motivic Aspects of Hodge Theory by : Chris Peters

Download or read book Motivic Aspects of Hodge Theory written by Chris Peters and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a series of lectures given at the Tata Institute of Fundamental Research, Mumbai, in 2007, on the theme of Hodge theoretic motives associated to various geometric objects. Starting with the topological setting, the notes go on to Hodge theory and mixed Hodge theory on the cohomology of varieties. Degenerations, limiting mixed Hodge structures and the relation to singularities are addressed next. The original proof of Bittner's theorem on the Grothendieck group of varieties, with some applications, is presented as an appendix to one of the chapters. The situation of relative varieties is addressed next using the machinery of mixed Hodge modules. Chern classes for singular varieties are explained in the motivic setting using Bittner's approach, and their full functorial meaning is made apparent using mixed Hodge modules. An appendix explains the treatment of Hodge characteristic in relation with motivic integration and string theory. Throughout these notes, emphasis is placed on explaining concepts and giving examples.

Singularity Theory I

Download Singularity Theory I PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3642580092
Total Pages : 250 pages
Book Rating : 4.6/5 (425 download)

DOWNLOAD NOW!


Book Synopsis Singularity Theory I by : V.I. Arnold

Download or read book Singularity Theory I written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact guide to the principles and main applications of Singularity Theory by one of the world’s top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. It’s ideal for any mathematician or physicist interested in modern mathematical analysis.

Singularities in Geometry and Topology

Download Singularities in Geometry and Topology PDF Online Free

Author :
Publisher :
ISBN 13 : 9814477044
Total Pages : pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!


Book Synopsis Singularities in Geometry and Topology by :

Download or read book Singularities in Geometry and Topology written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singularities

Download Singularities PDF Online Free

Author :
Publisher : Birkhäuser
ISBN 13 : 3034887701
Total Pages : 475 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!


Book Synopsis Singularities by : Vladimir I. Arnold

Download or read book Singularities written by Vladimir I. Arnold and published by Birkhäuser. This book was released on 2012-12-06 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.

Mixed Hodge Structures

Download Mixed Hodge Structures PDF Online Free

Author :
Publisher :
ISBN 13 : 9783540846277
Total Pages : 488 pages
Book Rating : 4.8/5 (462 download)

DOWNLOAD NOW!


Book Synopsis Mixed Hodge Structures by : Chris A. M. Peters

Download or read book Mixed Hodge Structures written by Chris A. M. Peters and published by . This book was released on 2008-08-12 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: