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Sheaves And Torsion Free Modules
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Book Synopsis Algebraic Cycles, Sheaves, Shtukas, and Moduli by : Piotr Pragacz
Download or read book Algebraic Cycles, Sheaves, Shtukas, and Moduli written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
Book Synopsis Algebraic Curves and One-Dimensional Fields by : Fedor Bogomolov
Download or read book Algebraic Curves and One-Dimensional Fields written by Fedor Bogomolov and published by American Mathematical Soc.. This book was released on 2002 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the essential topics in the geometry of algebraic curves, such as line and vector bundles, the Riemann-Roch Theorem, divisors, coherent sheaves, and zeroth and first cohomology groups. It demonstrates how curves can act as a natural introduction to algebraic geometry.
Book Synopsis Torsion-Free Modules by : Eben Matlis
Download or read book Torsion-Free Modules written by Eben Matlis and published by University of Chicago Press. This book was released on 1972 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory. The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied. An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.
Book Synopsis The Geometry of Moduli Spaces of Sheaves by : Daniel Huybrechts
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.
Book Synopsis Coherent Analytic Sheaves by : H. Grauert
Download or read book Coherent Analytic Sheaves written by H. Grauert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C.R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E.N.S
Book Synopsis Periodic Monopoles and Difference Modules by : Takuro Mochizuki
Download or read book Periodic Monopoles and Difference Modules written by Takuro Mochizuki and published by Springer Nature. This book was released on 2022-02-23 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity. The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson. This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.
Book Synopsis Lectures on Vector Bundles by : J. Le Potier
Download or read book Lectures on Vector Bundles written by J. Le Potier and published by Cambridge University Press. This book was released on with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Manifolds, Sheaves, and Cohomology by : Torsten Wedhorn
Download or read book Manifolds, Sheaves, and Cohomology written by Torsten Wedhorn and published by Springer. This book was released on 2016-07-25 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
Book Synopsis Algebraic Surfaces and Holomorphic Vector Bundles by : Robert Friedman
Download or read book Algebraic Surfaces and Holomorphic Vector Bundles written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
Download or read book Sheaf Theory written by Glen E. Bredon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems", the parts of sheaf theory covered here are those areas important to algebraic topology. Among the many innovations in this book, the concept of the "tautness" of a subspace is introduced and exploited; the fact that sheaf theoretic cohomology satisfies the homotopy property is proved for general topological spaces; and relative cohomology is introduced into sheaf theory. A list of exercises at the end of each chapter helps students to learn the material, and solutions to many of the exercises are given in an appendix. This new edition of a classic has been substantially rewritten and now includes some 80 additional examples and further explanatory material, as well as new sections on Cech cohomology, the Oliver transfer, intersection theory, generalised manifolds, locally homogeneous spaces, homological fibrations and p- adic transformation groups. Readers should have a thorough background in elementary homological algebra and in algebraic topology.
Book Synopsis An Introduction to Invariants and Moduli by : Shigeru Mukai
Download or read book An Introduction to Invariants and Moduli written by Shigeru Mukai and published by Cambridge University Press. This book was released on 2003-09-08 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample Text
Book Synopsis Non-commutative Algebraic Geometry by : F.M.J. van Oystaeyen
Download or read book Non-commutative Algebraic Geometry written by F.M.J. van Oystaeyen and published by Springer. This book was released on 2006-11-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Geometry by : Peter E. Newstead
Download or read book Algebraic Geometry written by Peter E. Newstead and published by CRC Press. This book was released on 1998-07-31 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a compendium of papers selected from the Europroj conferences held in Catania and Barcelona. The text contains research in algebraic geometry with emphasis on classification problems, and in particular studies on the structure of moduli spaces of vector bundles, and on the classification of curves and surfaces.
Book Synopsis An Invitation to Modern Enumerative Geometry by : Andrea T. Ricolfi
Download or read book An Invitation to Modern Enumerative Geometry written by Andrea T. Ricolfi and published by Springer Nature. This book was released on 2022-12-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research “beginners” in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
Book Synopsis Stable Module Theory by : Maurice Auslander
Download or read book Stable Module Theory written by Maurice Auslander and published by American Mathematical Soc.. This book was released on 1969 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notions of torsion and torsion freeness have played a very important role in module theory--particularly in the study of modules over integral domains. Furthermore, the use of homological techniques in this connection has been well established. It is the aim of this paper to extend these techniques and to show that this extension leads naturally to several new concepts (e.g. k-torsion freeness and Gorenstein dimension) which are useful in the classification of modules and rings.
Book Synopsis Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry by : Jean H Gallier
Download or read book Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry written by Jean H Gallier and published by World Scientific. This book was released on 2022-01-19 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
