Counting 3-uple Veronese surfaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910707341066240 |
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| author | Deopurkar, Anand Patel, Anand |
| author_facet | Deopurkar, Anand Patel, Anand |
| contents | This paper culminates in the count of the number of 3-Veronese surfaces passing through 13 general points. This follows the case of 2-Veronese surfaces discovered by Coble in the 1920's. One important element of the calculation is a direct construction of a space of "complete triangles." Our construction is different from the classical ordered constructions of Schubert, Collino and Fulton, as it occurs directly on the Hilbert scheme of length 3 subschemes of the plane. We transport the enumerative problem into a 26-dimensional Grassmannian bundle over our space of complete triangles, where we perform Atiyah-Bott localization. Several important questions arise, which we collect at the end of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting 3-uple Veronese surfaces Deopurkar, Anand Patel, Anand Algebraic Geometry 14N10, 14N25, 14N15, 51N35 This paper culminates in the count of the number of 3-Veronese surfaces passing through 13 general points. This follows the case of 2-Veronese surfaces discovered by Coble in the 1920's. One important element of the calculation is a direct construction of a space of "complete triangles." Our construction is different from the classical ordered constructions of Schubert, Collino and Fulton, as it occurs directly on the Hilbert scheme of length 3 subschemes of the plane. We transport the enumerative problem into a 26-dimensional Grassmannian bundle over our space of complete triangles, where we perform Atiyah-Bott localization. Several important questions arise, which we collect at the end of the paper. |
| title | Counting 3-uple Veronese surfaces |
| topic | Algebraic Geometry 14N10, 14N25, 14N15, 51N35 |
| url | https://arxiv.org/abs/2411.14232 |