On the Abelian fivefolds attached to cubic surfaces

To a family of smooth projective cubic surfaces one can canonically associate a family of abelian fivefolds. In characteristic zero, we calculate the Hodge groups of the abelian varieties which arise in this way. In arbitrary characteristic, we calculate the monodromy group of the universal family of abelian varieties, and thus show that the Galois group of the 27 lines on a general cubic surface in positive characteristic is as large as possible.

2010 Mathematics Subject Classification

Primary 14J10. Secondary 11G18, 14D05, 14K30.

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Published 28 April 2014