Rigid and stably balanced curves on Calabi-Yau and general-type hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909148309880832 |
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| author | Ran, Ziv |
| author_facet | Ran, Ziv |
| contents | A curve $C$ on a variety $X$ is stably balanced if the slopes of the Harder-Narasimhan filtration of its normal bundle $N$ are contained in an interval of length 1. For each $d\geq n+1$ we construct some regular families of pairs $(C, X)$ of the expected dimension with $X$ a hypersurface of degree $d$ in $\mathbb P^n$ and $C$ a stably balanced rigid curve on $X$, such that the family of hypersurfaces $X$ is smooth codimension $h^1(N)$ in the space of hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05410 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigid and stably balanced curves on Calabi-Yau and general-type hypersurfaces Ran, Ziv Algebraic Geometry 14j70, 14j32 A curve $C$ on a variety $X$ is stably balanced if the slopes of the Harder-Narasimhan filtration of its normal bundle $N$ are contained in an interval of length 1. For each $d\geq n+1$ we construct some regular families of pairs $(C, X)$ of the expected dimension with $X$ a hypersurface of degree $d$ in $\mathbb P^n$ and $C$ a stably balanced rigid curve on $X$, such that the family of hypersurfaces $X$ is smooth codimension $h^1(N)$ in the space of hypersurfaces. |
| title | Rigid and stably balanced curves on Calabi-Yau and general-type hypersurfaces |
| topic | Algebraic Geometry 14j70, 14j32 |
| url | https://arxiv.org/abs/2209.05410 |