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MARC 21

Recent Progress on the Donaldson–Thomas Theory: Wall-Crossing and Refined Invariants /
Tag	Description
020	$a9789811678387$9978-981-16-7838-7
082	$a530.15$223
099	$aOnline resource: Springer
100	$aToda, Yukinobu.$eauthor.$4aut$4http://id.loc.gov/vocabulary/relators/aut
245	$aRecent Progress on the Donaldson–Thomas Theory$h[EBook] :$bWall-Crossing and Refined Invariants /$cby Yukinobu Toda.
250	$a1st ed. 2021.
260	$aSingapore :$bSpringer Singapore :$bImprint: Springer,$c2021.
300	$aVIII, 104 p. 3 illus.$bonline resource.
336	$atext$btxt$2rdacontent
337	$acomputer$bc$2rdamedia
338	$aonline resource$bcr$2rdacarrier
440	$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v43
505	$a1Donaldson–Thomas invariants on Calabi–Yau 3-folds -- 2Generalized Donaldson–Thomas invariants -- 3Donaldson–Thomas invariants for quivers with super-potentials -- 4Donaldson–Thomas invariants for Bridgeland semistable objects -- 5Wall-crossing formulas of Donaldson–Thomas invariants -- 6Cohomological Donaldson–Thomas invariants -- 7Gopakumar–Vafa invariants -- 8Some future directions.
520	$aThis book is an exposition of recent progress on the Donaldson–Thomas (DT) theory. The DT invariant was introduced by R. Thomas in 1998 as a virtual counting of stable coherent sheaves on Calabi–Yau 3-folds. Later, it turned out that the DT invariants have many interesting properties and appear in several contexts such as the Gromov–Witten/Donaldson–Thomas conjecture on curve-counting theories, wall-crossing in derived categories with respect to Bridgeland stability conditions, BPS state counting in string theory, and others. Recently, a deeper structure of the moduli spaces of coherent sheaves on Calabi–Yau 3-folds was found through derived algebraic geometry. These moduli spaces admit shifted symplectic structures and the associated d-critical structures, which lead to refined versions of DT invariants such as cohomological DT invariants. The idea of cohomological DT invariants led to a mathematical definition of the Gopakumar–Vafa invariant, which was first proposed by Gopakumar–Vafa in 1998, but its precise mathematical definition has not been available until recently. This book surveys the recent progress on DT invariants and related topics, with a focus on applications to curve-counting theories.
533	$nMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
710	$aSpringerLink (Online service)
830	$aSpringerBriefs in Mathematical Physics,$x2197-1765 ;$v43
856	$uhttps://doi.org/10.1007/978-981-16-7838-7