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arXiv · 2209.05410

Rigid and stably balanced curves on Calabi-Yau and general-type hypersurfaces

Ziv Ran
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Abstract

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.

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Ziv Ran. 2022-09-12. Rigid and stably balanced curves on Calabi-Yau and general-type hypersurfaces. https://arxiv.org/abs/2209.05410

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