  In this paper, we construct certain algebraic correspondences between genus
three curves and certain type of Calabi-Yau threefolds which is double
coverings of three dimensional projective space. Via this correspondences, the
first cohomology groups of the curves can be embedded into the third cohomology
groups of the Calabi-Yau three folds. Moreover we prove that the cokernel of
this inclusion of variations ofHodge structures can not be a factor of any
variations of Hodge structures comming from polarized abelian schemes.
