A category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu }$-singularity

We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu }\text{-}$singularity. The semi-universal deformation of the $A_{\mu }\text{-}$singularity is given by a certain deformation of the polynomial of type $A_{\mu }$. In this paper, we consider the category of graded matrix factorizations associated to this deformed polynomial for a fixed parameter. To do so, we introduce a formal variable to make the polynomial homogeneous. As our main result, we construct a full strongly exceptional collection in this category for a generic parameter.