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

Format:

Book

Author/Creator:

Toda, Yukinobu, 1979- author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2350.

Lecture notes in mathematics, 0075-8434 ; 2350

Language:

English

Subjects (All):

Geometry, Algebraic.

Algebra, Homological.

Mathematical physics.

Physical Description:

xi, 309 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

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."-- Provided by publisher.

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

Categorified Hall products on DT categories

Some auxiliary results.

Notes:

Includes bibliographical references (pages 299-304) and index.

ISBN:

9783031617041

3031617045

OCLC:

1450340787