LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	530.15
Title	Recent Progress on the Donaldson–Thomas Theory ([EBook] :) : Wall-Crossing and Refined Invariants / / by Yukinobu Toda.
Author	Toda, Yukinobu
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2021.
Publication	Singapore : : Springer Singapore : : Imprint: Springer, , 2021.
Physical Details	VIII, 104 p. 3 illus. : online resource.
Series	SpringerBriefs in Mathematical Physics 2197-1765 ; ; 43
ISBN	9789811678387
Summary Note	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.:
Contents note	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.
Mode of acces to digital resource	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-981-16-7838-7
Links to Related Works	Subject References: Algebra, Homological . Algebraic Geometry . Category Theory, Homological Algebra . Mathematical Physics . Authors: author . Toda, Yukinobu . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematical Physics . Classification: 530.15 .

Catalogue Display

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

Reviews