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arXiv · 1710.03531

Fujita decomposition and Hodge loci

Paola Frediani·Alessandro Ghigi·Gian Pietro Pirola
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Abstract

This paper contains two results on Hodge loci in the moduli space of curves. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibres and the fibration is non-trivial, an appropriate exterior power of the cohomology of the fiber admits a Hodge substructure. In the case of curves it follows that the moduli image of the fibers is contained in a proper Hodge locus. The second result deals with divisors in the moduli space of curves. It is proved that the image of a divisor in the moduli of principally polarized abelian varieties is not contained in a proper totally geodesic subvariety. It follows that a Hodge locus in the moduli space of curves has codimension at least 2.

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Paola Frediani, Alessandro Ghigi, Gian Pietro Pirola. 2017-10-10. Fujita decomposition and Hodge loci. https://doi.org/10.1017/s1474748018000452

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