C∞-Algebraic Geometry with Corners

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.

• Pioneering work extending the existing theory of C∞-algebraic geometry and introducing readers to 'C∞-schemes with corners'
• Provides extensive background on the topic of manifolds with corners, allowing readers to develop understanding of an important topic rarely treated
• Presents material equipping readers with new tools for research in the areas of symplectic geometry and Floer theory