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On the L2-Hodge theory of Landau-Ginzburg models.
- Source :
-
Advances in Mathematics . Feb2022, Vol. 396, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f -twisted Sobolev spaces for the pair (X , f) and prove the corresponding Hodge-to-de Rham degeneration property via L 2 -Hodge theoretical methods when f satisfies an asymptotic condition of strongly ellipticity. This leads to a Frobenius manifold via the Barannikov-Kontsevich construction, unifying the Landau-Ginzburg and Calabi-Yau geometry. Our construction can be viewed as a generalization of K. Saito's higher residue and primitive form theory for isolated singularities. As an application, we construct Frobenius manifolds for orbifold Landau-Ginzburg B-models which admit crepant resolutions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 396
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 154895947
- Full Text :
- https://doi.org/10.1016/j.aim.2021.108165