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 'infini...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2024
|
| Schriftenreihe: | London Mathematical Society lecture note series
490 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-634 DE-92 URL des Erstveröffentlichers |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 10 Jan 2024) |
| Beschreibung: | 1 online resource (vi, 216 pages) digital, PDF file(s) |
| ISBN: | 9781009400190 |
| DOI: | 10.1017/9781009400190 |
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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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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 15 |
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| discipline | Mathematik |
| doi_str_mv | 10.1017/9781009400190 |
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| id | DE-604.BV049663292 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T07:28:50Z |
| institution | BVB |
| isbn | 9781009400190 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035006475 |
| oclc_num | 1437845303 |
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| owner_facet | DE-12 DE-92 DE-634 |
| physical | 1 online resource (vi, 216 pages) digital, PDF file(s) |
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| publishDate | 2024 |
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| publisher | Cambridge University Press |
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| series2 | London Mathematical Society lecture note series |
| spelling | Francis-Staite, Kelli (DE-588)1317633873 aut C∞-algebraic geometry with corners Kelli Francis-Staite, Dominic Joyce C-infinity-algebraic geometry with corners Cambridge Cambridge University Press 2024 1 online resource (vi, 216 pages) digital, PDF file(s) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 490 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 Geometry, Algebraic Joyce, Dominic D. 1968- (DE-588)1043994483 aut Erscheint auch als Druck-Ausgabe 978-1-009-40016-9 https://doi.org/10.1017/9781009400190 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Francis-Staite, Kelli Joyce, Dominic D. 1968- C∞-algebraic geometry with corners Geometry, Algebraic |
| title | C∞-algebraic geometry with corners |
| title_alt | C-infinity-algebraic geometry with corners |
| title_auth | C∞-algebraic geometry with corners |
| title_exact_search | C∞-algebraic geometry with corners |
| title_full | C∞-algebraic geometry with corners Kelli Francis-Staite, Dominic Joyce |
| title_fullStr | C∞-algebraic geometry with corners Kelli Francis-Staite, Dominic Joyce |
| title_full_unstemmed | C∞-algebraic geometry with corners Kelli Francis-Staite, Dominic Joyce |
| title_short | C∞-algebraic geometry with corners |
| title_sort | c∞ algebraic geometry with corners |
| topic | Geometry, Algebraic |
| topic_facet | Geometry, Algebraic |
| url | https://doi.org/10.1017/9781009400190 |
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