A category of graded matrix factorizations of a deformed polynomial associated to the $A_μ$-singularity
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914569033613312 |
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| author | Nakatani, Tomoya |
| author_facet | Nakatani, Tomoya |
| contents | We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_μ\textrm{-}$singularity. The semi-universal deformation of the $A_μ\textrm{-}$singularity is given by a certain deformation of the polynomial of type $A_μ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15878 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A category of graded matrix factorizations of a deformed polynomial associated to the $A_μ$-singularity Nakatani, Tomoya Algebraic Geometry Commutative Algebra Representation Theory 14, 13 We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_μ\textrm{-}$singularity. The semi-universal deformation of the $A_μ\textrm{-}$singularity is given by a certain deformation of the polynomial of type $A_μ$. 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. |
| title | A category of graded matrix factorizations of a deformed polynomial associated to the $A_μ$-singularity |
| topic | Algebraic Geometry Commutative Algebra Representation Theory 14, 13 |
| url | https://arxiv.org/abs/2605.15878 |