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Recent Progress on the Donaldson–Thomas Theory = Wall-Crossing and Refined Invariants /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Recent Progress on the Donaldson–Thomas Theory/ by Yukinobu Toda.
Reminder of title:	Wall-Crossing and Refined Invariants /
Author:	Toda, Yukinobu.
Description:	VIII, 104 p. 3 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical physics. -
Online resource:	https://doi.org/10.1007/978-981-16-7838-7
ISBN:	9789811678387

Recent Progress on the Donaldson–Thomas Theory = Wall-Crossing and Refined Invariants /
Toda, Yukinobu.

Recent Progress on the Donaldson–Thomas TheoryWall-Crossing and Refined Invariants /[electronic resource] :by Yukinobu Toda. - 1st ed. 2021. - VIII, 104 p. 3 illus.online resource. - SpringerBriefs in Mathematical Physics,432197-1765 ;. - SpringerBriefs in Mathematical Physics,8.

1Donaldson–Thomas invariants on Calabi–Yau 3-folds -- 2Generalized Donaldson–Thomas invariants -- 3Donaldson–Thomas invariants for quivers with super-potentials -- 4Donaldson–Thomas invariants for Bridgeland semistable objects -- 5Wall-crossing formulas of Donaldson–Thomas invariants -- 6Cohomological Donaldson–Thomas invariants -- 7Gopakumar–Vafa invariants -- 8Some future directions.

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.

ISBN: 9789811678387

Standard No.: 10.1007/978-981-16-7838-7doiSubjects--Topical Terms:

527831
Mathematical physics.

LC Class. No.: QA401-425

Dewey Class. No.: 530.15

Recent Progress on the Donaldson–Thomas Theory = Wall-Crossing and Refined Invariants /
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