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arXiv · 1301.1142

On the PSL(2,19)-invariant cubic sevenfold

Atanas Iliev·Xavier Roulleau
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Abstract

It has been proved by Adler that there exists a unique cubic hypersurface X in P^8 which is invariant under the action of the simple group PSL(2,19). In the present note we study the intermediate Jacobian of X and in particular we prove that the subjacent 85-dimensional torus is an Abelian variety. The symmetry group G=PSL(2,19) defines uniquely a G-invariant abelian 9-fold A(X), which we study in detail and describe its period lattice.

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Atanas Iliev, Xavier Roulleau. 2013-01-07. On the PSL(2,19)-invariant cubic sevenfold. https://arxiv.org/abs/1301.1142

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