Hermite Reciprocity and Self-Duality of Generalized Eagon-Northcott Complexes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917981813997568 |
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| author | Reed, Ethan |
| author_facet | Reed, Ethan |
| contents | Previous examples of self-duality for generalized Eagon-Northcott complexes were given by computing the divisor class group for Hankel determinantal rings. We prove a new case of self-duality of generalized Eagon-Northcott complexes with input being a map defining a Koszul module with nice properties. This choice of Koszul module can be specialized to the Weyman module, which was used in a proof of the generic version of Green's conjecture. In this case, the proof uses a version of Hermite Reciprocity not previously defined in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07184 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hermite Reciprocity and Self-Duality of Generalized Eagon-Northcott Complexes Reed, Ethan Commutative Algebra Algebraic Geometry 13D02, 13D07, 14F06, 15A69, 18G40, 20G05 Previous examples of self-duality for generalized Eagon-Northcott complexes were given by computing the divisor class group for Hankel determinantal rings. We prove a new case of self-duality of generalized Eagon-Northcott complexes with input being a map defining a Koszul module with nice properties. This choice of Koszul module can be specialized to the Weyman module, which was used in a proof of the generic version of Green's conjecture. In this case, the proof uses a version of Hermite Reciprocity not previously defined in the literature. |
| title | Hermite Reciprocity and Self-Duality of Generalized Eagon-Northcott Complexes |
| topic | Commutative Algebra Algebraic Geometry 13D02, 13D07, 14F06, 15A69, 18G40, 20G05 |
| url | https://arxiv.org/abs/2504.07184 |