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Algebraic correspondences between genus three curves and certain Calabi-Yau varieties
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 1, February 2010
- pp. 181-200
- 10.1353/ajm.0.0090
- Article
- Additional Information
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In this paper, we construct certain algebraic correspondences between
genus three curves and certain type of Calabi-Yau threefolds which are
double coverings of three dimensional projective spaces. Via this
correspondence, 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 of Hodge
structures cannot be a factor of any variations of Hodge structures
comming from polarized abelian schemes.