1# Library to Find Best eBook for Read
Author : Dominic D. Joyce
Release : 2019
Genre : Differentiable functions
Kind : eBook
Book Rating : 367/5 ( reviews)
Book Synopsis Algebraic Geometry Over C[infinity]-rings by : Dominic D. Joyce
Download or read book Algebraic Geometry Over C[infinity]-rings written by Dominic D. Joyce. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kelli Francis-Staite
Release : 2023-12-31
Genre : Mathematics
Kind : eBook
Book Rating : 207/5 ( reviews)
Book Synopsis C∞-Algebraic Geometry with Corners by : Kelli Francis-Staite
Download or read book C∞-Algebraic Geometry with Corners written by Kelli Francis-Staite. This book was released on 2023-12-31. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Dominic Joyce
Release : 2019-09-05
Genre :
Kind : eBook
Book Rating : 450/5 ( reviews)
Book Synopsis Algebraic Geometry over C∞-Rings by : Dominic Joyce
Download or read book Algebraic Geometry over C∞-Rings written by Dominic Joyce. This book was released on 2019-09-05. 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 : A. Granja
Release : 2001-05-08
Genre : Mathematics
Kind : eBook
Book Rating : 962/5 ( reviews)
Book Synopsis Ring Theory And Algebraic Geometry by : A. Granja
Download or read book Ring Theory And Algebraic Geometry written by A. Granja. This book was released on 2001-05-08. 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
Release : 1979-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 45X/5 ( reviews)
Book Synopsis Partially Ordered Rings and Semi-Algebraic Geometry by : Gregory W. Brumfiel
Download or read book Partially Ordered Rings and Semi-Algebraic Geometry written by Gregory W. Brumfiel. This book was released on 1979-12-20. 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.
