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  3. C∞-Algebraic Geometry with Corners
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  • Publisher:
    Cambridge University Press
    Publication date:
    January 2024
    January 2024
    ISBN:
    9781009400190
    9781009400169
    DOI:
    https://doi.org/10.1017/9781009400190
    Dimensions:
    Weight & Pages:
    Dimensions:
    (229 x 152 mm)
    Weight & Pages:
    0.32kg, 220 Pages
    • Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (490)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (490)
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    Book description

    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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