Téléchargez le livre : Recent Progress on the Donaldson–Thomas Theory

Recent Progress on the Donaldson–Thomas Theory

Wall-Crossing and Refined Invariants de

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Springer


Collection :

SpringerBriefs in Mathematical Physics

Paru le : 2021-12-15

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Description
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 firstproposed 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.
Pages
104 pages
Collection
SpringerBriefs in Mathematical Physics
Parution
2021-12-15
Marque
Springer
EAN papier
9789811678370
EAN PDF
9789811678387
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
10
Taille du fichier
1956 Ko
Prix
68,56 €
EAN EPUB
9789811678387
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
10
Taille du fichier
7229 Ko
Prix
68,56 €

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