Recent Progress on the Donaldson–Thomas Theory
ebook ∣ Wall-Crossing and Refined Invariants · SpringerBriefs in Mathematical Physics
By Yukinobu Toda
Sign up to save your library
With an OverDrive account, you can save your favorite libraries for at-a-glance information about availability. Find out more about OverDrive accounts.
Find this title in Libby, the library reading app by OverDrive.
Search for a digital library with this title
Title found at these libraries:
Loading... |
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.
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.