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Measures of irrationality of the Fano surface of a cubic threefold by Gounelas, Frank; Kouvidakis, Alexis is a scholarly article available to read on EtoBox.

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For $X$ a smooth cubic threefold we study the Pl\"ucker 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.

Author

Gounelas, Frank; Kouvidakis, Alexis

Published

2017

Language

EN