Algebraic Geometry Over C Rings
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Author |
: Dominic D. Joyce |
Publisher |
: |
Total Pages |
: 139 |
Release |
: 2019 |
ISBN-10 |
: 1470453363 |
ISBN-13 |
: 9781470453367 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Algebraic Geometry Over C[infinity]-rings by : Dominic D. Joyce
Author |
: Dominic Joyce |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 139 |
Release |
: 2019-09-05 |
ISBN-10 |
: 9781470436452 |
ISBN-13 |
: 1470436450 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Algebraic Geometry over C∞-Rings by : Dominic Joyce
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 |
Total Pages |
: 224 |
Release |
: 2023-12-31 |
ISBN-10 |
: 9781009400206 |
ISBN-13 |
: 1009400207 |
Rating |
: 4/5 (06 Downloads) |
Synopsis C∞-Algebraic Geometry with Corners by : Kelli Francis-Staite
Schemes in algebraic geometry can have singular points, whereas differential geometers typically focus on manifolds which are nonsingular. However, there is a class of schemes, 'C∞-schemes', which allow differential geometers to study a huge range of singular spaces, including 'infinitesimals' and infinite-dimensional spaces. These are applied in synthetic differential geometry, and derived differential geometry, the study of 'derived manifolds'. Differential geometers also study manifolds with corners. The cube is a 3-dimensional manifold with corners, with boundary the six square faces. This book introduces 'C∞-schemes with corners', singular spaces in differential geometry with good notions of boundary and corners. They can be used to define 'derived manifolds with corners' and 'derived orbifolds with corners'. These have applications to major areas of symplectic geometry involving moduli spaces of J-holomorphic curves. This work will be a welcome source of information and inspiration for graduate students and researchers working in differential or algebraic geometry.
Author |
: A. Granja |
Publisher |
: CRC Press |
Total Pages |
: 366 |
Release |
: 2001-05-08 |
ISBN-10 |
: 0203907965 |
ISBN-13 |
: 9780203907962 |
Rating |
: 4/5 (65 Downloads) |
Synopsis Ring Theory And Algebraic Geometry by : A. Granja
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 |
: C. Musili |
Publisher |
: Springer |
Total Pages |
: 349 |
Release |
: 2001-03-15 |
ISBN-10 |
: 9789386279057 |
ISBN-13 |
: 9386279053 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Algebraic Geometry for Beginners by : C. Musili
Author |
: Donu Arapura |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 326 |
Release |
: 2012-02-15 |
ISBN-10 |
: 9781461418092 |
ISBN-13 |
: 1461418097 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Algebraic Geometry over the Complex Numbers by : Donu Arapura
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
Author |
: R. Kaya |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 567 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9789400954601 |
ISBN-13 |
: 9400954603 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Rings and Geometry by : R. Kaya
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 |
: Hiroaki Hijikata |
Publisher |
: Academic Press |
Total Pages |
: 417 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483265186 |
ISBN-13 |
: 1483265188 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Algebraic Geometry and Commutative Algebra by : Hiroaki Hijikata
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 |
: Thiruvalloor E. Venkata Balaji |
Publisher |
: Universitätsverlag Göttingen |
Total Pages |
: 241 |
Release |
: 2010 |
ISBN-10 |
: 9783941875326 |
ISBN-13 |
: 3941875329 |
Rating |
: 4/5 (26 Downloads) |
Synopsis An Introduction to Families, Deformations and Moduli by : Thiruvalloor E. Venkata Balaji
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 |
: Robin Hartshorne |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 511 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9781475738490 |
ISBN-13 |
: 1475738498 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Algebraic Geometry by : Robin Hartshorne
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.