Hodge structures for orbifold cohomology

dc.creatorFernandez, Javier
dc.date2003-11-03
dc.date2006-05-16
dc.date.accessioned2026-07-07T06:35:47Z
dc.date.available2026-07-07T06:35:47Z
dc.descriptionWe construct a polarized Hodge structure on the primitive part of Chen and Ruan's orbifold cohomology $H_{orb}^k(X)$ for projective $SL$-orbifolds $X$ satisfying a ``Hard Lefschetz Condition''. Furthermore, the total cohomology $H_{orb}^{*,*}(X)$ forms a mixed Hodge structure that is polarized by every element of the Kähler cone of $X$. Using results of Cattani-Kaplan-Schmid this implies the existence of an abstract polarized variation of Hodge structure on the complexified Kähler cone of $X$. This construction should be considered as the analogue of the abstract polarized variation of Hodge structure that can be attached to the singular cohomology of a crepant resolution of $X$, in the light of the conjectural correspondence between the (quantum) orbifold cohomology and the (quantum) cohomology of a crepant resolution.
dc.descriptionStreamlined exposition. Added examples. Final version
dc.identifierhttps://arxiv.org/abs/math/0311026
dc.identifierhttp://arxiv.org/abs/math/0311026
dc.identifierProc. Amer. Math. Soc. 134 (2006), no. 9, 2511-2520
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99899
dc.subjectAlgebraic Geometry
dc.titleHodge structures for orbifold cohomology
dc.typetext

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