Hilbert schemes of rational curves on Fano hypersurfaces

Bin Wang

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arXiv · 1501.06070

Hilbert schemes of rational curves on Fano hypersurfaces

Bin Wang

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Abstract

In this paper we try to further explore the linear model of the moduli of rational maps. Our attempt yields following results. Let $X\subset \mathbf P^n$ be a generic hypersurface of degree $h$. Let $R_d(X, h)$ denote the open set of the Hilbert scheme parameterizing irreducible rational curves of degree $d$ on $X$. We obtain that (1) If $4\leq h\leq n-1$, $R_d(X, h)$ is an integral, local complete intersection of dimension \begin{equation} (n+1-h)d+n-4. \end{equation} (2) If furthermore $(h^2-n)d+h\leq 0$ and $h\geq 4$, in addition to part (1), $R_d(X, h)$ is also rationally connected.

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BibTeX RIS

Bin Wang. 2015-01-24. Hilbert schemes of rational curves on Fano hypersurfaces. https://arxiv.org/abs/1501.06070

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