1.

Record Nr.

UNINA9910513578303321

Autore

Toda Yukinobu

Titolo

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

Pubbl/distr/stampa

Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2021

ISBN

981-16-7838-3

Edizione

[1st ed. 2021.]

Descrizione fisica

1 online resource (110 pages)

Collana

SpringerBriefs in Mathematical Physics, , 2197-1765 ; ; 43

Disciplina

512.55

Soggetti

Mathematical physics

Geometry, Algebraic

Algebra, Homological

Mathematical Physics

Algebraic Geometry

Category Theory, Homological Algebra

Invariants

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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.