Maximally nodal sextic surfaces and linear determinantal representations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918461166321664 |
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| author | Cho, Yonghwa |
| author_facet | Cho, Yonghwa |
| contents | We prove that every maximally nodal sextic surface\,(with 65 nodes) $X \subset \mathbb{P}_{\mathbb{C}}^3$ contains a symmetric half-even set of nodes of cardinality 35. It follows that the associated half-quadratic sheaf is the cokernel of a symmetric $6 \times 6$ matrix of linear forms, yielding a linear determinantal representation of $X$. In particular, after a suitable Serre twist, the half-quadratic sheaf is an Ulrich sheaf of rank 1. As an example, we exhibit an explicit $6 \times 6$ matrix of linear forms whose determinant defines the Barth sextic surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20114 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximally nodal sextic surfaces and linear determinantal representations Cho, Yonghwa Algebraic Geometry We prove that every maximally nodal sextic surface\,(with 65 nodes) $X \subset \mathbb{P}_{\mathbb{C}}^3$ contains a symmetric half-even set of nodes of cardinality 35. It follows that the associated half-quadratic sheaf is the cokernel of a symmetric $6 \times 6$ matrix of linear forms, yielding a linear determinantal representation of $X$. In particular, after a suitable Serre twist, the half-quadratic sheaf is an Ulrich sheaf of rank 1. As an example, we exhibit an explicit $6 \times 6$ matrix of linear forms whose determinant defines the Barth sextic surface. |
| title | Maximally nodal sextic surfaces and linear determinantal representations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.20114 |