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C∞-algebraic geometry with corners

Record Type:	Language materials, printed : Monograph/item
Title/Author:	C∞-algebraic geometry with corners/ Kelli Francis-Staite, Dominic Joyce.
Author:	Francis-Staite, Kelli.
other author:	Joyce, Dominic D.
Published:	Cambridge :Cambridge University Press, : 2024.,
Description:	vi, 216 p. :ill., digital ; : 23 cm.;
Notes:	Title from publisher's bibliographic system (viewed on 10 Jan 2024).
Subject:	Geometry, Algebraic. -
Online resource:	https://doi.org/10.1017/9781009400190
ISBN:	9781009400190

C∞-algebraic geometry with corners
Francis-Staite, Kelli.

C∞-algebraic geometry with corners[electronic resource] /Kelli Francis-Staite, Dominic Joyce. - Cambridge :Cambridge University Press,2024. - vi, 216 p. :ill., digital ;23 cm. - London Mathematical Society lecture note series ;490. - London Mathematical Society lecture note series ;382..

Title from publisher's bibliographic system (viewed on 10 Jan 2024).

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.

ISBN: 9781009400190Subjects--Topical Terms:

580393
Geometry, Algebraic.

LC Class. No.: QA564 / .F73 2024

Dewey Class. No.: 516.35

C∞-algebraic geometry with corners
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520 $a 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.
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