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arXiv · 2201.09793

Interpolation of curves on Fano hypersurfaces

Ziv Ran
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Abstract

On a general hypersurface of degree $d\leq n$ in $\mathbb P^n$ or $\mathbb P^n$ itself, we prove the existence of curves of any genus and high enough degree depending on the genus passing through the expected number $t$ of general points or incident to a general collection of subvarieties of suitable codimensions. In some cases we also show that the family of curves through $t$ fixed points has general moduli as family of $t$-pointed curves. These results imply positivity of certain intersection numbers on Kontsevich spaces of stable maps. An arithmetical appendix by M. C. Chang descibes the set of numerical characters ($n, d$, curve degree, genus) to which our results apply.

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Ziv Ran. 2022-01-24. Interpolation of curves on Fano hypersurfaces. https://arxiv.org/abs/2201.09793

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