03724nam 22006255 450 991051357830332120240214155116.0981-16-7838-310.1007/978-981-16-7838-7(MiAaPQ)EBC6827721(Au-PeEL)EBL6827721(CKB)20151344300041(OCoLC)1290022695(DE-He213)978-981-16-7838-7(PPN)259387509(EXLCZ)992015134430004120211215d2021 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierRecent Progress on the Donaldson–Thomas Theory Wall-Crossing and Refined Invariants /by Yukinobu Toda1st ed. 2021.Singapore :Springer Nature Singapore :Imprint: Springer,2021.1 online resource (110 pages)SpringerBriefs in Mathematical Physics,2197-1765 ;43Print version: Toda, Yukinobu Recent Progress on the Donaldson-Thomas Theory Singapore : Springer Singapore Pte. Limited,c2022 9789811678370 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.SpringerBriefs in Mathematical Physics,2197-1765 ;43Mathematical physicsGeometry, AlgebraicAlgebra, HomologicalMathematical PhysicsAlgebraic GeometryCategory Theory, Homological AlgebraInvariantsthubLlibres electrònicsthubMathematical physics.Geometry, Algebraic.Algebra, Homological.Mathematical Physics.Algebraic Geometry.Category Theory, Homological Algebra.Invariants512.55Toda Yukinobu1071417MiAaPQMiAaPQMiAaPQBOOK9910513578303321Recent Progress on the Donaldson–Thomas Theory3562081UNINA