03211nam 22005655 450 991087218920332120240706125242.09783031617058(electronic bk.)978303161704110.1007/978-3-031-61705-8(MiAaPQ)EBC31518795(Au-PeEL)EBL31518795(CKB)32674597900041(DE-He213)978-3-031-61705-8(EXLCZ)993267459790004120240706d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierCategorical Donaldson-Thomas Theory for Local Surfaces /by Yukinobu Toda1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (318 pages)Lecture Notes in Mathematics,1617-9692 ;2350Print version: Toda, Yukinobu Categorical Donaldson-Thomas Theory for Local Surfaces Cham : Springer International Publishing AG,c2024 9783031617041 - 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.Lecture Notes in Mathematics,1617-9692 ;2350Algebraic geometryAlgebra, HomologicalMathematical physicsAlgebraic GeometryCategory Theory, Homological AlgebraMathematical PhysicsAlgebraic geometry.Algebra, Homological.Mathematical physics.Algebraic Geometry.Category Theory, Homological Algebra.Mathematical Physics.516.35Toda Yukinobu1071417MiAaPQMiAaPQMiAaPQ9910872189203321Categorical Donaldson-Thomas Theory for Local Surfaces4174529UNINA