Recent Progress on the Donaldson–Thomas Theory eBook
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Recent Progress on the Donaldson–Thomas Theory

Wall-Crossing and Refined Invariants

Yukinobu Toda


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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.

About the book
Author
Yukinobu  Toda
Imprint
Springer
Collection
SpringerBriefs in Mathematical Physics
Publication date
2021-12-15
Pages
104 pages
Print ISBN
9789811678370
Language
English
Ebook informations
EAN PDF
9789811678387
Price
£54.99
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Copy count 1
Print count 10
File size 1956 Ko
Ce livre est accessible aux handicaps   Informations accessibility
EAN EPUB
9789811678387
Price
£54.99
Read more
Copy count 1
Print count 10
File size 7229 Ko
Ce livre est accessible aux handicaps   Informations accessibility
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