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Viser: Câ??-Algebraic Geometry with Corners
Câ??-Algebraic Geometry with Corners
Kelli Francis-Staite og Dominic D. Joyce
(2024)
Sprog: Engelsk
Cambridge University Press
835,00 kr.
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Detaljer om varen
- Paperback: 220 sider
- Udgiver: Cambridge University Press (Januar 2024)
- Forfattere: Kelli Francis-Staite og Dominic D. Joyce
- ISBN: 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.or graduate students and researchers working in differential or algebraic geometry.or graduate students and researchers working in differential or algebraic geometry.or graduate students and researchers working in differential or algebraic geometry.
1. Introduction;
2. Background on C-schemes
3. Background on manifolds with (g-)corners;
4. (Pre) C-rings with corners;
5. C-schemes with corners;
6. Boundaries, corners, and the corner functor;
7. Modules, and sheaves of modules;
8. Further generalizations and applications; References; Glossary of Notation; Index.
2. Background on C-schemes
3. Background on manifolds with (g-)corners;
4. (Pre) C-rings with corners;
5. C-schemes with corners;
6. Boundaries, corners, and the corner functor;
7. Modules, and sheaves of modules;
8. Further generalizations and applications; References; Glossary of Notation; Index.
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