Categorical Donaldson-Thomas theory for local surfaces:
This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the...
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| Format: | Book |
| Language: | English |
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Cham, Switzerland
Springer
[2024]
|
| Series: | Lecture notes in mathematics
Volume 2350 |
| Subjects: | |
| Summary: | This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas |
| Physical Description: | xi, 309 Seiten Diagramme |
| ISBN: | 9783031617041 |
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| 505 | 8 | |a Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results | |
| 520 | |a This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas | ||
| 650 | 4 | |a Donaldson-Thomas invariants | |
| 650 | 4 | |a Invariants de Donaldson-Thomas | |
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| contents | Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results |
| ctrlnum | (OCoLC)1450346181 (DE-599)BVBBV049790955 |
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| id | DE-604.BV049790955 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-07T00:07:29Z |
| institution | BVB |
| isbn | 9783031617041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035131734 |
| oclc_num | 1450346181 |
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| owner | DE-188 DE-83 |
| owner_facet | DE-188 DE-83 |
| physical | xi, 309 Seiten Diagramme |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Toda, Yukinobu (DE-588)1337567361 aut Categorical Donaldson-Thomas theory for local surfaces Yukinobu Toda Cham, Switzerland Springer [2024] © 2024 xi, 309 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2350 Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas Donaldson-Thomas invariants Invariants de Donaldson-Thomas Original Erscheint auch als Online-Ausgabe 978-3-031-61705-8 Lecture notes in mathematics Volume 2350 (DE-604)BV000676446 2350 |
| spellingShingle | Toda, Yukinobu Categorical Donaldson-Thomas theory for local surfaces Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results Donaldson-Thomas invariants Invariants de Donaldson-Thomas Lecture notes in mathematics |
| title | Categorical Donaldson-Thomas theory for local surfaces |
| title_auth | Categorical Donaldson-Thomas theory for local surfaces |
| title_exact_search | Categorical Donaldson-Thomas theory for local surfaces |
| title_full | Categorical Donaldson-Thomas theory for local surfaces Yukinobu Toda |
| title_fullStr | Categorical Donaldson-Thomas theory for local surfaces Yukinobu Toda |
| title_full_unstemmed | Categorical Donaldson-Thomas theory for local surfaces Yukinobu Toda |
| title_short | Categorical Donaldson-Thomas theory for local surfaces |
| title_sort | categorical donaldson thomas theory for local surfaces |
| topic | Donaldson-Thomas invariants Invariants de Donaldson-Thomas |
| topic_facet | Donaldson-Thomas invariants Invariants de Donaldson-Thomas |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT todayukinobu categoricaldonaldsonthomastheoryforlocalsurfaces |