Recent Progress on the Donaldson Thomas Theory is popular PDF and ePub book, written by Yukinobu Toda in 2021-12-15, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, Recent Progress on the Donaldson Thomas Theory can be Read Online from any device for your convenience.
Recent Progress on the Donaldson Thomas Theory Book PDF Summary
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.
Detail Book of Recent Progress on the Donaldson Thomas Theory PDF
- Author : Yukinobu Toda
- Release : 15 December 2021
- Publisher : Springer Nature
- ISBN : 9789811678387
- Genre : Science
- Total Page : 110 pages
- Language : English
- PDF File Size : 15,6 Mb
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