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020 _a9783031617058
_9978-3-031-61705-8
024 7 _a10.1007/978-3-031-61705-8
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
100 1 _aToda, Yukinobu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980144
245 1 0 _aCategorical Donaldson-Thomas Theory for Local Surfaces
_h[electronic resource] /
_cby Yukinobu Toda.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXI, 312 p. 159 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2350
505 0 _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.
520 _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.
650 0 _aAlgebraic geometry.
650 0 _aAlgebra, Homological.
_970150
650 0 _aMathematical physics.
650 1 4 _aAlgebraic Geometry.
650 2 4 _aCategory Theory, Homological Algebra.
_970155
650 2 4 _aMathematical Physics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031617041
776 0 8 _iPrinted edition:
_z9783031617065
830 0 _aLecture Notes in Mathematics,
_x1617-9692 ;
_v2350
_975434
856 4 0 _uhttps://doi.org/10.1007/978-3-031-61705-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-LNM
999 _c61399
_d61399