Cellular free resolutions for normalizations of toric ideals
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908723437371392 |
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| author | Berkesch, Christine Heller, Lauren Cranton Smith, Gregory G. Yang, Jay |
| author_facet | Berkesch, Christine Heller, Lauren Cranton Smith, Gregory G. Yang, Jay |
| contents | For any toric ideal $I$ in a polynomial ring $S$, we provide a combinatorial description of a free resolution of the integral closure of the $S$-module $S/I$. These new complexes arise from an extension of Bayer--Sturmfels' theory of cellular free resolutions. As applications, we unify several constructions for a resolution of the diagonal embedding of a toric variety, and compare the locally free resolutions for toric subvarieties introduced by Hanlon--Hicks--Lazarev and Brown--Erman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cellular free resolutions for normalizations of toric ideals Berkesch, Christine Heller, Lauren Cranton Smith, Gregory G. Yang, Jay Commutative Algebra Algebraic Geometry 13D02, 14M25, 05E14 For any toric ideal $I$ in a polynomial ring $S$, we provide a combinatorial description of a free resolution of the integral closure of the $S$-module $S/I$. These new complexes arise from an extension of Bayer--Sturmfels' theory of cellular free resolutions. As applications, we unify several constructions for a resolution of the diagonal embedding of a toric variety, and compare the locally free resolutions for toric subvarieties introduced by Hanlon--Hicks--Lazarev and Brown--Erman. |
| title | Cellular free resolutions for normalizations of toric ideals |
| topic | Commutative Algebra Algebraic Geometry 13D02, 14M25, 05E14 |
| url | https://arxiv.org/abs/2512.17871 |