The classification of ACM curves on a surface in $\mathbb{P}^{3}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915779076685824 |
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| author | Castorena, Abel Vite, Montserrat |
| author_facet | Castorena, Abel Vite, Montserrat |
| contents | We classify ACM curves contained in a surface of degree d in $\mathbb{P}^{3}$ in terms of weak admissible pairs. In the case of a very general smooth determinantal quartic surface, we provide a geometric description of these curves and compute their Picard classes on the surface. Finally, we present a generalization to ACM closed subvarieties of codimension $1$ on a hypersurface in $\mathbb{P}^{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The classification of ACM curves on a surface in $\mathbb{P}^{3}$ Castorena, Abel Vite, Montserrat Algebraic Geometry We classify ACM curves contained in a surface of degree d in $\mathbb{P}^{3}$ in terms of weak admissible pairs. In the case of a very general smooth determinantal quartic surface, we provide a geometric description of these curves and compute their Picard classes on the surface. Finally, we present a generalization to ACM closed subvarieties of codimension $1$ on a hypersurface in $\mathbb{P}^{n}$. |
| title | The classification of ACM curves on a surface in $\mathbb{P}^{3}$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2602.06141 |