C∞-Algebraic Geometry with Corners (Paperback) (ISBN-13: 9781009400169)

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: Kelli Francis-Staite,Dominic Joyce
ISBN-10: 1009400169
ISBN-13: 9781009400169
Publisher: Cambridge University Press
Language: English
Published: 01/04/2024
Pages: 220
Format: Paperback
Weight: 0.80lbs
Size: 8.98h x 5.98w x 0.47d