Recent Progress on the Donaldson-Thomas Theory - Wall-Crossing and Refined Invariants (Paperback, 1st ed. 2021)

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.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Series:	SpringerBriefs in Mathematical Physics, 43
Release date:	December 2021
First published:	2021
Authors:	Yukinobu Toda
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	104
Edition:	1st ed. 2021
ISBN-13:	978-981-16-7837-0
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	981-16-7837-5
Barcode:	9789811678370

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