Measures of irrationality of the Fano surface of a cubic threefold

2017/07/04 by Gounelas, Frank, Kouvidakis, Alexis · 2 citations
#14H10 #14J30 #14M15 #14M20 #14N20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.00853

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 ℙ², is six.

Cited by

• A primer on measures of irrationality
• Moduli space of genus one curves on cubic threefold

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• Irrationality of threefolds via Weil's conjectures