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arXiv · 2308.02089

Polarized interpolation and normal postulation for curves on Fano hypersurfaces

Ziv Ran
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Abstract

A general hypersurface $X$ of degree $\leq n$ in projective space contains curves $C$ of any genus $g\geq 0$ and sufficiently large degree depnding on $g$ whose normal and conormal bundles have good postulation or natural cohomology in the sense that each twist has either $H^0=0$ or $H^1=0$. This implies a polarized version of the interpolation property for $C$ on $X$.

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Ziv Ran. 2023-08-04. Polarized interpolation and normal postulation for curves on Fano hypersurfaces. https://arxiv.org/abs/2308.02089

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