Conjectured mirror of the augmented hypersurface \hat f is a toric Landau–Ginzburg model

Demonstrate that the hypersurface in (C*)^{n+1} defined by \hat f(x_1,…,x_{n+1}) = f(x_1,…,x_n) + x_{n+1} = 0 is mirror to the toric Landau–Ginzburg model (\hat Y, \hat W) = (C × Y, y W), where y is the coordinate on the C factor.

Background

The text discusses extending the mirror correspondence by embedding the complement as a hypersurface in a higher-dimensional torus via \hat f, and proposes a specific toric Landau–Ginzburg model (C × Y, yW) as the mirror.

This conjectural identification links the geometry of the hypersurface to a product LG model whose singularity category is expected to match that of Z = W−1(0), following Orlov’s equivalence.