The $G$-Noncommutative Minimal Model Program
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910031175221248 |
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| author | Wu, Dongjian Zhang, Nantao |
| author_facet | Wu, Dongjian Zhang, Nantao |
| contents | In this paper, we study the $G$-equivariant noncommutative minimal model program ($G$-NMMP), as an equivariant generalization of the framework introduced in arXiv:2301.13168. The aim of this program is to construct quasi-convergent paths in the spaces of Bridgeland stability conditions on derived categories of $G$-equivariant coherent sheaves. For finite groups, we employ induction techniques to construct such paths from the non-equivariant setting. In the setting of algebraic group actions, we introduce the notion of $\mathbb T$-stability conditions to reformulate the proposal, and then we construct quasi-convergent paths for equivariant projective spaces from small quantum cohomology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20335 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $G$-Noncommutative Minimal Model Program Wu, Dongjian Zhang, Nantao Algebraic Geometry Mathematical Physics Category Theory In this paper, we study the $G$-equivariant noncommutative minimal model program ($G$-NMMP), as an equivariant generalization of the framework introduced in arXiv:2301.13168. The aim of this program is to construct quasi-convergent paths in the spaces of Bridgeland stability conditions on derived categories of $G$-equivariant coherent sheaves. For finite groups, we employ induction techniques to construct such paths from the non-equivariant setting. In the setting of algebraic group actions, we introduce the notion of $\mathbb T$-stability conditions to reformulate the proposal, and then we construct quasi-convergent paths for equivariant projective spaces from small quantum cohomology. |
| title | The $G$-Noncommutative Minimal Model Program |
| topic | Algebraic Geometry Mathematical Physics Category Theory |
| url | https://arxiv.org/abs/2602.20335 |