An Introduction To Families Deformations And Moduli

Author : Thiruvalloor E. Venkata Balaji
Publisher : Universitätsverlag Göttingen
ISBN 13 : 3941875329
Total Pages : 241 pages
Book Rating : 4.26/5 ( download)

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Download or read book An Introduction to Families, Deformations and Moduli written by Thiruvalloor E. Venkata Balaji and published by Universitätsverlag Göttingen. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.

Author : Kenji Ueno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821565
Total Pages : 328 pages
Book Rating : 4.63/5 ( download)

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Download or read book Advances in Moduli Theory written by Kenji Ueno and published by American Mathematical Soc.. This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word ``moduli'' in the sense of this book first appeared in the epoch-making paper of B. Riemann, Theorie der Abel'schen Funktionen, published in 1857. Riemann defined a Riemann surface of an algebraic function field as a branched covering of a one-dimensional complex projective space, and found out that Riemann surfaces have parameters. This work gave birth to the theory of moduli. However, the viewpoint regarding a Riemann surface as an algebraic curve became the mainstream,and the moduli meant the parameters for the figures (graphs) defined by equations. In 1913, H. Weyl defined a Riemann surface as a complex manifold of dimension one. Moreover, Teichmuller's theory of quasiconformal mappings and Teichmuller spaces made a start for new development of the theory ofmoduli, making possible a complex analytic approach toward the theory of moduli of Riemann surfaces. This theory was then investigated and made complete by Ahlfors, Bers, Rauch, and others. However, the theory of Teichmuller spaces utilized the special nature of complex dimension one, and it was difficult to generalize it to an arbitrary dimension in a direct way. It was Kodaira-Spencer's deformation theory of complex manifolds that allowed one to study arbitrary dimensional complex manifolds.Initial motivation in Kodaira-Spencer's discussion was the need to clarify what one should mean by number of moduli. Their results, together with further work by Kuranishi, provided this notion with intrinsic meaning. This book begins by presenting the Kodaira-Spencer theory in its original naiveform in Chapter 1 and introduces readers to moduli theory from the viewpoint of complex analytic geometry. Chapter 2 briefly outlines the theory of period mapping and Jacobian variety for compact Riemann surfaces, with the Torelli theorem as a goal. The theory of period mappings for compact Riemann surfaces can be generalized to the theory of period mappings in terms of Hodge structures for compact Kahler manifolds. In Chapter 3, the authors state the theory of Hodge structures, focusingbriefly on period mappings. Chapter 4 explains conformal field theory as an application of moduli theory. This is the English translation of a book originally published in Japanese. Other books by Kenji Ueno published in this AMS series, Translations of Mathematical Monographs, include An Introduction toAlgebraic Geometry, Volume 166, Algebraic Geometry 1: From Algebraic Varieties to Schemes, Volume 185, and Algebraic Geometry 2: Sheaves and Cohomology, Volume 197.

Author : Marco Manetti
Publisher : Springer Nature
ISBN 13 : 9811911851
Total Pages : 576 pages
Book Rating : 4.59/5 ( download)

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Download or read book Lie Methods in Deformation Theory written by Marco Manetti and published by Springer Nature. This book was released on 2022-08-01 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective. Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer–Cartan equations. The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory. Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

Author : Joe Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387227377
Total Pages : 381 pages
Book Rating : 4.75/5 ( download)

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Download or read book Moduli of Curves written by Joe Harris and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A guide to a rich and fascinating subject: algebraic curves and how they vary in families. Providing a broad but compact overview of the field, this book is accessible to readers with a modest background in algebraic geometry. It develops many techniques, including Hilbert schemes, deformation theory, stable reduction, intersection theory, and geometric invariant theory, with the focus on examples and applications arising in the study of moduli of curves. From such foundations, the book goes on to show how moduli spaces of curves are constructed, illustrates typical applications with the proofs of the Brill-Noether and Gieseker-Petri theorems via limit linear series, and surveys the most important results about their geometry ranging from irreducibility and complete subvarieties to ample divisors and Kodaira dimension. With over 180 exercises and 70 figures, the book also provides a concise introduction to the main results and open problems about important topics which are not covered in detail.

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1139485822
Total Pages : 345 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Author : Robert H. Dijkgraaf
Publisher : Springer Science & Business Media
ISBN 13 : 1461242649
Total Pages : 570 pages
Book Rating : 4.42/5 ( download)

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Download or read book The Moduli Space of Curves written by Robert H. Dijkgraaf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.

Author : Javier Fernández de Bobadilla
Publisher : American Mathematical Society
ISBN 13 : 1470470535
Total Pages : 110 pages
Book Rating : 4.31/5 ( download)

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Download or read book Reflexive Modules on Normal Gorenstein Stein Surfaces, Their Deformations and Moduli written by Javier Fernández de Bobadilla and published by American Mathematical Society. This book was released on 2024-07-25 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Author : Olivier Debarre
Publisher : Springer Science & Business Media
ISBN 13 : 147575406X
Total Pages : 245 pages
Book Rating : 4.63/5 ( download)

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Download or read book Higher-Dimensional Algebraic Geometry written by Olivier Debarre and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.

Author : Leticia Brambila
Publisher : Cambridge University Press
ISBN 13 : 1107636388
Total Pages : 347 pages
Book Rating : 4.85/5 ( download)

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Download or read book Moduli Spaces written by Leticia Brambila and published by Cambridge University Press. This book was released on 2014-03-13 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.

Author : Edoardo Sernesi
Publisher : Springer Science & Business Media
ISBN 13 : 3540306153
Total Pages : 343 pages
Book Rating : 4.53/5 ( download)

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Download or read book Deformations of Algebraic Schemes written by Edoardo Sernesi and published by Springer Science & Business Media. This book was released on 2007-04-20 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.