Syzygies of secant varieties of curves of genus 2
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914784788611072 |
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| author | Li, Li |
| author_facet | Li, Li |
| contents | Ein, Niu and Park showed in [ENP20] that if the degree of the line bundle $L$ on a curve of genus $g$ is at least $2g+2k+1$, the $k$-th secant variety of the curve via the embedding defined by the complete linear system of $L$ is normal, projectively normal and arithmetically Cohen-Macaulay, and they also proved some vanishing of the Betti diagrams. However, the length of the linear strand of weight $k+1$ of the resolution of the secant variety $Σ_k$ of a curve of $g\geq2$ is still mysterious. In this paper we calculate the complete Betti diagrams of the secant varieties of curves of genus $2$ using Boij-Söderberg theory. The main idea is to find the pure diagrams that contribute to the Betti diagram of the secant variety via calculating some special positions of the Betti diagram. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Syzygies of secant varieties of curves of genus 2 Li, Li Algebraic Geometry 14N07(Primary) 14H45, 13D02(Secondary) Ein, Niu and Park showed in [ENP20] that if the degree of the line bundle $L$ on a curve of genus $g$ is at least $2g+2k+1$, the $k$-th secant variety of the curve via the embedding defined by the complete linear system of $L$ is normal, projectively normal and arithmetically Cohen-Macaulay, and they also proved some vanishing of the Betti diagrams. However, the length of the linear strand of weight $k+1$ of the resolution of the secant variety $Σ_k$ of a curve of $g\geq2$ is still mysterious. In this paper we calculate the complete Betti diagrams of the secant varieties of curves of genus $2$ using Boij-Söderberg theory. The main idea is to find the pure diagrams that contribute to the Betti diagram of the secant variety via calculating some special positions of the Betti diagram. |
| title | Syzygies of secant varieties of curves of genus 2 |
| topic | Algebraic Geometry 14N07(Primary) 14H45, 13D02(Secondary) |
| url | https://arxiv.org/abs/2305.02479 |