Goppa Duality for Surfaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912645827788800 |
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| author | Iwasaki, Hikari |
| author_facet | Iwasaki, Hikari |
| contents | Gale duality is an involution of point configurations in projective spaces. Goppa duality extends this concept to a duality between linear series on a Gorenstein curve passing through prescribed points. We generalize this classical result to surfaces, establishing a duality for linear series on surfaces realizing prescribed points as a complete intersection of two divisors. We present several applications, including existence and uniqueness results for Veronese surfaces satisfying conditions to pass through given points or curves. As a key example, we give an alternative proof of Coble's result on the existence of four Veronese surfaces passing through nine general points in projective 5-space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Goppa Duality for Surfaces Iwasaki, Hikari Algebraic Geometry 14N10 Gale duality is an involution of point configurations in projective spaces. Goppa duality extends this concept to a duality between linear series on a Gorenstein curve passing through prescribed points. We generalize this classical result to surfaces, establishing a duality for linear series on surfaces realizing prescribed points as a complete intersection of two divisors. We present several applications, including existence and uniqueness results for Veronese surfaces satisfying conditions to pass through given points or curves. As a key example, we give an alternative proof of Coble's result on the existence of four Veronese surfaces passing through nine general points in projective 5-space. |
| title | Goppa Duality for Surfaces |
| topic | Algebraic Geometry 14N10 |
| url | https://arxiv.org/abs/2510.11951 |