  We study certain toric Gorenstein varieties with isolated singularities which
are the quotient spaces of generic unimodular representations by the
one-dimensional torus, or by the product of the one-dimensional torus with a
finite abelian group. Based on the works of \v{S}penko and Van den Bergh
[Invent. Math. 210 (2017), no. 1, 3-67] and Mori and Ueyama [Adv. Math. 297
(2016), 54-92], we show that the singularity categories of these varieties
admit tilting objects, and hence are triangle equivalent to the perfect
categories of some finite dimensional algebras.
