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arXiv · 2605.15878

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

Tomoya Nakatani
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Abstract

We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu}\textrm{-}$singularity. The semi-universal deformation of the $A_{\mu}\textrm{-}$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.

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Tomoya Nakatani. 2026-05-15. A category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu}$-singularity. https://arxiv.org/abs/2605.15878

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