This paper contains two results on Hodge loci in M_g. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers 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 fiber is contained in a proper Hodge locus. The second result deals with divisors in M_g. It is proved that the image under the period map of a divisor in M_g is not contained in a proper totally geodesic subvariety of A_g. It follows that a Hodge locus in Mg has codimension at least 2.
Fujita decomposition and Hodge loci
Paola Frediani;Alessandro Ghigi;Gian Pietro Pirola
2020-01-01
Abstract
This paper contains two results on Hodge loci in M_g. The first concerns fibrations over curves with a non-trivial flat part in the Fujita decomposition. If local Torelli theorem holds for the fibers 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 fiber is contained in a proper Hodge locus. The second result deals with divisors in M_g. It is proved that the image under the period map of a divisor in M_g is not contained in a proper totally geodesic subvariety of A_g. It follows that a Hodge locus in Mg has codimension at least 2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
