Friday, March 29, 2013

1303.7126 (Huai-Liang Chang et al.)

Witten's top Chern class via cosection localization    [PDF]

Huai-Liang Chang, Jun Li, Wei-Ping Li
For a Landau Ginzburg space ([C^n/G],W), we construct the Witten's top Chern classes as algebraic cycles via cosection localized virtual cycles in case all sectors are narrow. We verify all axioms of such classes. We derive an explicit formula of such classes in the free case. We prove that this construction is equivalent to the prior constructions of Polishchuk-Vaintrob, of Chiodo and of Fan-Jarvis-Ruan.
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