On the abelian fivefolds attached to cubic surfaces

Abstract

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 suitably general cubic surface in positive characteristic is as large as possible.

Fixed classification of Hodge groups; other small edits

References in corpus (2)

• The integral monodromy of hyperelliptic and trielliptic curves
• Cubic Surfaces with Special Periods

Cited by in corpus (1)

• Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution