03014nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001400172072001700186072002300203072001600226100008400242245010300326250001800429264006900447300004400516336002600560337002600586338003600612347002400648490005300672505029200725520102301017650002402040650003302064650002602097650002402123650004902147650002602196710003402222773002602256776003602282776003602318830006002354856004602414912001402460912001502474912001402489999001702503978-3-031-61705-8DE-He21320251030112617.0cr nn 008mamaa240706s2024    sz |    s    |||| 0|eng d  a97830316170589978-3-031-61705-87 a10.1007/978-3-031-61705-82doi 4aQA564-609 7aPBMW2bicssc 7aMAT0120102bisacsh 7aPBMW2thema1 aToda, Yukinobu.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut98014410aCategorical Donaldson-Thomas Theory for Local Surfacesh[electronic resource] /cby Yukinobu Toda.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXI, 312 p. 159 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23500 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.  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. 0aAlgebraic geometry. 0aAlgebra, Homological.970150 0aMathematical physics.14aAlgebraic Geometry.24aCategory Theory, Homological Algebra.97015524aMathematical Physics.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303161704108iPrinted edition:z9783031617065 0aLecture Notes in Mathematics,x1617-9692 ;v235097543440uhttps://doi.org/10.1007/978-3-031-61705-8  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c61399d61399