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Recent progress on the Donaldson-Thomas theorywall-crossing and refined invariants /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Recent progress on the Donaldson-Thomas theoryby Yukinobu Toda.
Reminder of title:	wall-crossing and refined invariants /
Author:	Toda, Yukinobu.
Published:	Singapore :Springer Singapore :2021.
Description:	viii, 104 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Donaldson-Thomas invariants.
Online resource:	https://doi.org/10.1007/978-981-16-7838-7
ISBN:	9789811678387$q(electronic bk.)

Recent progress on the Donaldson-Thomas theorywall-crossing and refined invariants /
Toda, Yukinobu.

Recent progress on the Donaldson-Thomas theorywall-crossing and refined invariants /[electronic resource] :by Yukinobu Toda. - Singapore :Springer Singapore :2021. - viii, 104 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v. 432197-1765 ;. - SpringerBriefs in mathematical physics ;v.1..

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$q(electronic bk.)

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

910929
Donaldson-Thomas invariants.

LC Class. No.: QA554 / .T63 2021

Dewey Class. No.: 516.5

Recent progress on the Donaldson-Thomas theorywall-crossing and refined invariants /
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520 $a 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.
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