Amazon cover image
Image from Amazon.com

Categorical Donaldson-Thomas theory for local surfaces / Yukinobu Toda.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 2350.Publisher: Cham : Springer, 2024Description: 1 online resource (xi, 312 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783031617058
  • 3031617053
Subject(s): Additional physical formats: Print version:: No titleDDC classification:
  • 516/.5 23/eng/20240711
LOC classification:
  • QA554
Online resources:
Contents:
Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results.
Summary: This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

Includes bibliographical references and index.

Introduction -- Koszul duality equivalence -- Categorical DT theory for local surfaces -- D-critical D/K equivalence conjectures -- Categorical wall-crossing via Koszul duality -- Window theorem for DT categories -- Categori ed Hall products on DT categories -- Some auxiliary results.

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas.

Online resource; title from PDF title page (SpringerLink, viewed July 11, 2024).

Powered by Koha