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Author : Dominic D. Joyce
Publisher :
ISBN 13 : 9781470453367
Total Pages : 139 pages
Book Rating : 4.63/5 ( download)
Download or read book Algebraic Geometry Over C[infinity]-rings written by Dominic D. Joyce and published by . This book was released on 2019 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dominic Joyce
Publisher : American Mathematical Soc.
ISBN 13 : 1470436450
Total Pages : 139 pages
Book Rating : 4.52/5 ( download)
Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce and published by American Mathematical Soc.. This book was released on 2019-09-05 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kelli Francis-Staite
Publisher : Cambridge University Press
ISBN 13 : 1009400169
Total Pages : 223 pages
Book Rating : 4.69/5 ( download)
Download or read book C?-Algebraic Geometry with Corners written by Kelli Francis-Staite and published by Cambridge University Press. This book was released on 2023-12-31 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crossing the boundary between differential and algebraic geometry in order to study singular spaces, this book introduces 'C∞-schemes with corners'.
Author : A. Granja
Publisher : CRC Press
ISBN 13 : 9780203907962
Total Pages : 366 pages
Book Rating : 4.65/5 ( download)
Download or read book Ring Theory And Algebraic Geometry written by A. Granja and published by CRC Press. This book was released on 2001-05-08 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Gregory W. Brumfiel
Publisher : Cambridge University Press
ISBN 13 : 052122845X
Total Pages : 293 pages
Book Rating : 4.59/5 ( download)
Download or read book Partially Ordered Rings and Semi-Algebraic Geometry written by Gregory W. Brumfiel and published by Cambridge University Press. This book was released on 1979-12-20 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hiroaki Hijikata
Publisher : Academic Press
ISBN 13 : 1483265188
Total Pages : 417 pages
Book Rating : 4.86/5 ( download)
Download or read book Algebraic Geometry and Commutative Algebra written by Hiroaki Hijikata and published by Academic Press. This book was released on 2014-05-10 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robin Hartshorne
Publisher : Springer Science & Business Media
ISBN 13 : 1475738498
Total Pages : 511 pages
Book Rating : 4.90/5 ( download)
Download or read book Algebraic Geometry written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.
Author : R. Kaya
Publisher : Springer Science & Business Media
ISBN 13 : 9400954603
Total Pages : 567 pages
Book Rating : 4.01/5 ( download)
Download or read book Rings and Geometry written by R. Kaya and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : André Weil
Publisher :
ISBN 13 : 9781470431761
Total Pages : 363 pages
Book Rating : 4.69/5 ( download)
Download or read book Foundations of Algebraic Geometry written by André Weil and published by . This book was released on 1946 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Author : C. Musili
Publisher : Springer
ISBN 13 : 9386279053
Total Pages : 349 pages
Book Rating : 4.57/5 ( download)
Download or read book Algebraic Geometry for Beginners written by C. Musili and published by Springer. This book was released on 2001-03-15 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt:
