Regular and rigid curves on some Calabi-Yau and general-type complete intersections
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917621226536960 |
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| author | Ran, Ziv |
| author_facet | Ran, Ziv |
| contents | Let $X$ be either a general hypersurface of degree $n+1$ in $\mathbb P^n$ or a general $(2,n)$ complete intersection in $\mathbb P^{n+1}, n\geq 4$. We construct balanced rational curves on $X$ of all high enough degrees. If $n=3$ or $g=1$, we construct rigid curves of genus $g$ on $X$ of all high enough degrees. As an application we construct some rigid bundles on Calabi-Yau threefolds. In addition, we construct some low-degree balanced rational curves on hypersurfaces of degree $n + 2$ in $\mathbb P^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_01096 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Regular and rigid curves on some Calabi-Yau and general-type complete intersections Ran, Ziv Algebraic Geometry Mathematical Physics Differential Geometry 14j30, 14j32, 14j60, 14j70 Let $X$ be either a general hypersurface of degree $n+1$ in $\mathbb P^n$ or a general $(2,n)$ complete intersection in $\mathbb P^{n+1}, n\geq 4$. We construct balanced rational curves on $X$ of all high enough degrees. If $n=3$ or $g=1$, we construct rigid curves of genus $g$ on $X$ of all high enough degrees. As an application we construct some rigid bundles on Calabi-Yau threefolds. In addition, we construct some low-degree balanced rational curves on hypersurfaces of degree $n + 2$ in $\mathbb P^n$. |
| title | Regular and rigid curves on some Calabi-Yau and general-type complete intersections |
| topic | Algebraic Geometry Mathematical Physics Differential Geometry 14j30, 14j32, 14j60, 14j70 |
| url | https://arxiv.org/abs/2207.01096 |