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arXiv · 1802.06261

Non-degeneracy of cohomological traces for general Landau-Ginzburg models

Dmitry Doryn·Calin Iuliu Lazaroiu
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Abstract

We prove non-degeneracy of the cohomological bulk and boundary traces for general open-closed Landau-Ginzburg models associated to a pair $(X,W)$, where $X$ is a non-compact complex manifold with trivial canonical line bundle and $W$ is a complex-valued holomorphic function defined on $X$, assuming only that the critical locus of $W$ is compact (but may not consist of isolated points). These results can be viewed as certain "deformed" versions of Serre duality. The first amounts to a duality property for the hypercohomology of the sheaf Koszul complex of $W$, while the second is equivalent with the statement that a certain power of the shift functor is a Serre functor on the even subcategory of the $\mathbb{Z}_2$-graded category of topological D-branes of such models.

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Dmitry Doryn, Calin Iuliu Lazaroiu. 2018-02-17. Non-degeneracy of cohomological traces for general Landau-Ginzburg models. https://doi.org/10.1007/s00220-022-04423-9

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