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arXiv · 2312.15317

The Fano variety of lines on singular cyclic cubic fourfolds

Samuel Boissière·Paola Comparin·Lucas Li Bassi
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Abstract

We study the symplectic resolution of the Fano variety of lines on some singular cyclic cubic fourfolds, i.e. cubic fourfolds arising as cyclic 3:1 cover of $\mathbb{P}^4$ branched along a cubic threefold. In particular we are interested in the geometry of these varieties in the case of cyclic cubic fourfolds branched along a cubic threefold having one isolated singularity of type $A_i$ for $i=2,3,4$. On these symplectic resolutions we find a non-symplectic automorphism of order three induced by the covering automorphism.

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Samuel Boissière, Paola Comparin, Lucas Li Bassi. 2023-12-23. The Fano variety of lines on singular cyclic cubic fourfolds. https://arxiv.org/abs/2312.15317

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