Hodge structures for orbifold cohomology
| dc.creator | Fernandez, Javier | |
| dc.date | 2003-11-03 | |
| dc.date | 2006-05-16 | |
| dc.date.accessioned | 2026-07-07T06:35:47Z | |
| dc.date.available | 2026-07-07T06:35:47Z | |
| dc.description | We 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.description | Streamlined exposition. Added examples. Final version | |
| dc.identifier | https://arxiv.org/abs/math/0311026 | |
| dc.identifier | http://arxiv.org/abs/math/0311026 | |
| dc.identifier | Proc. Amer. Math. Soc. 134 (2006), no. 9, 2511-2520 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99899 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Hodge structures for orbifold cohomology | |
| dc.type | text |