LEADER 03211nam 22005655 450 001 9910872189203321 005 20240706125242.0 010 $a9783031617058$b(electronic bk.) 010 $z9783031617041 024 7 $a10.1007/978-3-031-61705-8 035 $a(MiAaPQ)EBC31518795 035 $a(Au-PeEL)EBL31518795 035 $a(CKB)32674597900041 035 $a(DE-He213)978-3-031-61705-8 035 $a(EXLCZ)9932674597900041 100 $a20240706d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCategorical Donaldson-Thomas Theory for Local Surfaces /$fby Yukinobu Toda 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (318 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2350 311 08$aPrint version: Toda, Yukinobu Categorical Donaldson-Thomas Theory for Local Surfaces Cham : Springer International Publishing AG,c2024 9783031617041 327 $a- 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. 330 $aThis book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry. The focus is on local surfaces, i.e. the total spaces of canonical line bundles on algebraic surfaces, which form an interesting class of Calabi-Yau 3-folds. Using Koszul duality equivalences and singular support theory, dg-categories are constructed which categorify Donaldson-Thomas invariants on local surfaces. The DT invariants virtually count stable coherent sheaves on Calabi-Yau 3-folds, and play an important role in modern enumerative geometry, representation theory and mathematical physics. Requiring a basic knowledge of algebraic geometry and homological algebra, this monograph is primarily addressed to researchers working in enumerative geometry, especially Donaldson-Thomas theory, derived categories of coherent sheaves, and related areas. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2350 606 $aAlgebraic geometry 606 $aAlgebra, Homological 606 $aMathematical physics 606 $aAlgebraic Geometry 606 $aCategory Theory, Homological Algebra 606 $aMathematical Physics 615 0$aAlgebraic geometry. 615 0$aAlgebra, Homological. 615 0$aMathematical physics. 615 14$aAlgebraic Geometry. 615 24$aCategory Theory, Homological Algebra. 615 24$aMathematical Physics. 676 $a516.35 700 $aToda$b Yukinobu$01071417 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910872189203321 996 $aCategorical Donaldson-Thomas Theory for Local Surfaces$94174529 997 $aUNINA