Algebraic correspondences between genus three curves and certain Calabi-Yau varieties

Abstract

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.