On the rationality of certain Fano threefolds

Ciro Ciliberto

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arXiv · 2306.04486

On the rationality of certain Fano threefolds

Ciro Ciliberto

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Abstract

In this paper I study the rationality problem for Fano threefolds $X\subset \p^{p+1}$ of genus $p$, that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus $p$ is rational as soon as $p\geq 8$ (this result has already been obtained in \cite {PCS}, but we give here an independent proof); (2) a non--trigonal Fano threefold of genus $p\geq 7$ containing a plane is rational; (3) any Fano threefold of genus $p\geq 17$ is rational; (4) a Fano threefold of genus $p\geq 12$ containing an ordinary line $\ell$ in its smooth locus is rational.

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Ciro Ciliberto. 2023-06-07. On the rationality of certain Fano threefolds. https://arxiv.org/abs/2306.04486

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