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arXiv · 1707.00853

Measures of irrationality of the Fano surface of a cubic threefold

Frank Gounelas·Alexis Kouvidakis
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Abstract

For $X$ a smooth cubic threefold we study the Plücker embedding of the Fano surface of lines $S$ of $X$. We prove that if $X$ is general then the minimal gonality of a covering family of curves of $S$ is four and that this happens for a unique family of curves. The analysis also shows that there is a unique pentagonal connecting family of curves, which leads to the fact that the connecting gonality of $S$ is five whereas the degree of irrationality, i.e.\ the minimal degree of a rational map from $S$ to $\mathbb{P}^2$, is six.

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Frank Gounelas, Alexis Kouvidakis. 2018-05-03. Measures of irrationality of the Fano surface of a cubic threefold. https://arxiv.org/abs/1707.00853

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