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  1. Bog
  2. Geometri
  3. Algebraisk geometri

Recent Progress on the Donaldson–Thomas Theory

- Wall-Crossing and Refined Invariants
Af: Yukinobu Toda Engelsk Paperback

Recent Progress on the Donaldson–Thomas Theory

- Wall-Crossing and Refined Invariants
Af: Yukinobu Toda Engelsk Paperback
Tjek vores konkurrenters priser
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.

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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.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 104
ISBN-13: 9789811678370
Indbinding: Paperback
Udgave:
ISBN-10: 9811678375
Kategori: Algebraisk geometri
Udg. Dato: 16 dec 2021
Længde: 11mm
Bredde: 234mm
Højde: 156mm
Forlag: Springer Verlag, Singapore
Oplagsdato: 16 dec 2021
Forfatter(e): Yukinobu Toda
Forfatter(e) Yukinobu Toda

Kategori Algebraisk geometri

ISBN-13 9789811678370

Sprog Engelsk

Indbinding Paperback

Sider 104

Udgave

Længde 11mm

Bredde 234mm

Højde 156mm

Udg. Dato 16 dec 2021

Oplagsdato 16 dec 2021

Forlag Springer Verlag, Singapore

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