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In this paper we describe a physical realization of a family of non-compactKahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburgmodels, motivated by some recent non-Kahler solutions of Strominger systems,and utilizing some recent ideas from GLSMs. We consider threefolds given asfiber products of compact genus g Riemann surfaces and noncompact threefolds.Each genus g Riemann surface is constructed using recent GLSM tricks, as adouble cover of P^1 branched over a degree 2g + 2 locus, realized vianonperturbative effects rather than as the critical locus of a superpotential.We focus in particular on special cases corresponding to a set of Kahlertwistor spaces of certain hyperKahler four-manifolds, specifically the twistorspaces of R^4, C^2/Z_k, and S^1 x R^3. We check in all cases that the conditionfor trivial canonical bundle arising physically matches the mathematicalconstraint.

Landau-Ginzburg models for certain fiber products with curves