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Author : Dominic D. Joyce
Publisher : Unknown
Page : 139 pages
File Size : 46,8 Mb
Release : 2019
Category : Differentiable functions
ISBN : 1470453363
Author : Kelli Francis-Staite,Dominic Joyce
Publisher : Cambridge University Press
Page : 223 pages
File Size : 45,7 Mb
Release : 2023-12-31
Category : Mathematics
ISBN : 9781009400169
Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.
Author : A. Granja,J.A. Hermida Alonso,A Verschoren
Publisher : CRC Press
Page : 366 pages
File Size : 47,6 Mb
Release : 2001-05-08
Category : Mathematics
ISBN : 0203907965
Focuses on the interaction between algebra and algebraic geometry, including high-level research papers and surveys contributed by over 40 top specialists representing more than 15 countries worldwide. Describes abelian groups and lattices, algebras and binomial ideals, cones and fans, affine and projective algebraic varieties, simplicial and cellular complexes, polytopes, and arithmetics.
Author : Dominic Joyce
Publisher : American Mathematical Soc.
Page : 139 pages
File Size : 49,8 Mb
Release : 2019-09-05
Category : Electronic
ISBN : 9781470436452
If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operation Φf:C∞(X)n→C∞(X) acting by Φf:(c1,…,cn)↦f(c1,…,cn), and these operations Φf satisfy many natural identities. Thus, C∞(X) actually has a far richer structure than the obvious R-algebra structure. The author explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by C∞-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are C∞-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps. The author also studies quasicoherent sheaves on C∞-schemes, and C∞-stacks, in particular Deligne-Mumford C∞-stacks, a 2-category of geometric objects generalizing orbifolds. Many of these ideas are not new: C∞-rings and C∞ -schemes have long been part of synthetic differential geometry. But the author develops them in new directions. In earlier publications, the author used these tools to define d-manifolds and d-orbifolds, “derived” versions of manifolds and orbifolds related to Spivak's “derived manifolds”.
Author : Gregory W. Brumfiel
Publisher : Cambridge University Press
Page : 293 pages
File Size : 55,6 Mb
Release : 1979-12-20
Category : Mathematics
ISBN : 9780521228459
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance.
Author : R. Kaya,P. Plaumann,K. Strambach
Publisher : Springer Science & Business Media
Page : 567 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400954601
When looking for applications of ring theory in geometry, one first thinks of algebraic geometry, which sometimes may even be interpreted as the concrete side of commutative algebra. However, this highly de veloped branch of mathematics has been dealt with in a variety of mono graphs, so that - in spite of its technical complexity - it can be regarded as relatively well accessible. While in the last 120 years algebraic geometry has again and again attracted concentrated interes- which right now has reached a peak once more - , the numerous other applications of ring theory in geometry have not been assembled in a textbook and are scattered in many papers throughout the literature, which makes it hard for them to emerge from the shadow of the brilliant theory of algebraic geometry. It is the aim of these proceedings to give a unifying presentation of those geometrical applications of ring theo~y outside of algebraic geometry, and to show that they offer a considerable wealth of beauti ful ideas, too. Furthermore it becomes apparent that there are natural connections to many branches of modern mathematics, e. g. to the theory of (algebraic) groups and of Jordan algebras, and to combinatorics. To make these remarks more precise, we will now give a description of the contents. In the first chapter, an approach towards a theory of non-commutative algebraic geometry is attempted from two different points of view.
Author : C. Musili
Publisher : Springer
Page : 349 pages
File Size : 49,8 Mb
Release : 2001-03-15
Category : Mathematics
ISBN : 9789386279057
Author : Keith Kendig
Publisher : Courier Dover Publications
Page : 320 pages
File Size : 46,6 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9780486801872
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry. 2015 edition.
Author : Stefaan Caenepeel
Publisher : CRC Press
Page : 128 pages
File Size : 54,7 Mb
Release : 2020-09-30
Category : Mathematics
ISBN : 9781000116731
"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "
Author : F. van Oystaeyen,A. Verschoren
Publisher : Springer
Page : 312 pages
File Size : 41,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540390572
Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 48,5 Mb
Release : 2021-09-10
Category : Electronic
ISBN : 1015107672
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author : A.N. Parshin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 53,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662036624
This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
Author : Günter Harder
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 41,7 Mb
Release : 2008-08-01
Category : Mathematics
ISBN : 9783834895011
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Author : Hiroaki Hijikata,Heisuke Hironaka,Masaki Maruyama
Publisher : Academic Press
Page : 417 pages
File Size : 48,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265186
Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from power series rings and rings of invariants of finite linear groups to the convolution algebra of distributions on totally disconnected locally compact groups. The discussion begins with a description of several formulas for enumerating certain types of objects, which may be tabular arrangements of integers called Young tableaux or some types of monomials. The next chapter explains how to establish these enumerative formulas, with emphasis on the role played by transformations of determinantal polynomials and recurrence relations satisfied by them. The book then turns to several applications of the enumerative formulas and universal identity, including including enumerative proofs of the straightening law of Doubilet-Rota-Stein and computations of Hilbert functions of polynomial ideals of certain determinantal loci. Invariant differentials and quaternion extensions are also examined, along with the moduli of Todorov surfaces and the classification problem of embedded lines in characteristic p. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.
Author : Jean Dieudonné
Publisher : CRC Press
Page : 202 pages
File Size : 40,6 Mb
Release : 1985-05-30
Category : Mathematics
ISBN : 0412993716
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.