Recent Progress on the Donaldson–Thomas Theory

Wall-Crossing and Refined Invariants

    • 46,99 €
    • 46,99 €

Description de l’éditeur

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.

GENRE
Science et nature
SORTIE
2021
15 décembre
LANGUE
EN
Anglais
LONGUEUR
112
Pages
ÉDITIONS
Springer Nature Singapore
TAILLE
4,5
Mo

Autres livres de cette série

2023
2022
2014
2014
2015
2015