Postulation for 2-superfat points in the plane
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912207153922048 |
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| author | Canino, Stefano Catalisano, Maria Virginia Gimigliano, Alessandro Ida, Monica Oneto, Alessandro |
| author_facet | Canino, Stefano Catalisano, Maria Virginia Gimigliano, Alessandro Ida, Monica Oneto, Alessandro |
| contents | We study the postulation of 0-dimensional schemes given by unions of 2-superfat points in general position in the plane, i.e., the union of local schemes defined by the intersection of two distinct double lines. We prove that such schemes have good postulation, i.e., they have the expected Hilbert function. We also show the good postulation of such schemes when we add a general 3-fat point. Finally, we use these results to answer a peculiar kind of interpolation problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Postulation for 2-superfat points in the plane Canino, Stefano Catalisano, Maria Virginia Gimigliano, Alessandro Ida, Monica Oneto, Alessandro Algebraic Geometry Commutative Algebra 14C20, 14N05 We study the postulation of 0-dimensional schemes given by unions of 2-superfat points in general position in the plane, i.e., the union of local schemes defined by the intersection of two distinct double lines. We prove that such schemes have good postulation, i.e., they have the expected Hilbert function. We also show the good postulation of such schemes when we add a general 3-fat point. Finally, we use these results to answer a peculiar kind of interpolation problem. |
| title | Postulation for 2-superfat points in the plane |
| topic | Algebraic Geometry Commutative Algebra 14C20, 14N05 |
| url | https://arxiv.org/abs/2501.16849 |