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Categorical Donaldson-Thomas theory for local surfaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	Categorical Donaldson-Thomas theory for local surfacesby Yukinobu Toda.
Author:	Toda, Yukinobu.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xi, 312 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Donaldson-Thomas invariants.
Online resource:	https://doi.org/10.1007/978-3-031-61705-8
ISBN:	9783031617058$q(electronic bk.)

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

Categorical Donaldson-Thomas theory for local surfaces[electronic resource] /by Yukinobu Toda. - Cham :Springer Nature Switzerland :2024. - xi, 312 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23501617-9692 ;. - Lecture notes in mathematics ;2035..

- 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.

ISBN: 9783031617058$q(electronic bk.)

Standard No.: 10.1007/978-3-031-61705-8doiSubjects--Topical Terms:

910929
Donaldson-Thomas invariants.

LC Class. No.: QA554

Dewey Class. No.: 516.5

Categorical Donaldson-Thomas theory for local surfaces
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520 $a 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.
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