Cantitate/Preț
Produs

Recent Progress on the Donaldson–Thomas Theory: Wall-Crossing and Refined Invariants: SpringerBriefs in Mathematical Physics, cartea 43

Autor Yukinobu Toda
en Limba Engleză Paperback – 16 dec 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 firstproposed 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.

Citește tot Restrânge

Din seria SpringerBriefs in Mathematical Physics

Preț: 46773 lei

Nou

Puncte Express: 702

Preț estimativ în valută:
8952 9305$ 7416£

Carte tipărită la comandă

Livrare economică 04-18 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9789811678370
ISBN-10: 9811678375
Pagini: 104
Ilustrații: VIII, 104 p. 3 illus.
Dimensiuni: 155 x 235 x 11 mm
Greutate: 0.17 kg
Ediția:1st ed. 2021
Editura: Springer Nature Singapore
Colecția Springer
Seria SpringerBriefs in Mathematical Physics

Locul publicării:Singapore, Singapore

Cuprins

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.

Recenzii

“The book is directed at readers with a solid foundation in algebraic geometry. … the main definitions and theorems are nicely illustrated by examples. … The book will serve as a guide to further reading for those wishing to learn more details about the theory.” (Matthew B. Young, Mathematical Reviews, March, 2023)

Notă biografică

The author is currently Professor and Principal investigator at Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo. He was an invited speaker at the ICM 2014.

Caracteristici

Provides an introduction of DT theory for both mathematicians and physicists Emphasizes both the foundation and computations in the study of DT theory Contains a mathematical theory of Gopakumar–Vafa invariants, a new subject not available in other survey works