Recent Progress on the Donaldson-Thomas Theory Wall-Crossing and Refined Invariants
This book is an exposition of recent progress on the Donaldson-Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi-Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in s...
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| Autor Corporativo: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
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Singapore :
Springer Singapore
2021.
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| Edición: | 1st ed. 2021. |
| Colección: | Springer eBooks.
SpringerBriefs in Mathematical Physics ; 43. |
| Acceso en línea: | Conectar con la versión electrónica |
| Ver en Universidad de Navarra: | https://innopac.unav.es/record=b45996702*spi |
| Sumario: | This book is an exposition of recent progress on the Donaldson-Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi-Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov-Witten/Donaldson-Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi-Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar-Vafa invariant, which was first proposed by Gopakumar-Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories. |
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| Descripción Física: | 1 recurso electrónico, VIII, 104 páginas, 3 ilustraciones |
| Formato: | Forma de acceso: World Wide Web. |
| ISBN: | 9789811678387 |
