In this chapter we classify all families C → Pn of covers with a pure (1, n) – VHS. Due to Theorem 4.4.4, all these families have a dense set of CM fibers. We say that a pure (1, n) – VHS is primitive, if the (1, n) eigenspace Lj satisfies that (formula presented). Otherwise the pure (1, n) – VHS is derived. In Section 6.1 we give an integral condition for the branch indices dk of the family C with the fibers given by (formula presented) This integral condition is stronger than the similar integral condition INT of P. Deligne and G. D. Mostow [18]. Thus we call this strong integral condition SINT. We show that this condition is necessary for the existence of a primitive pure (1, n) – VHS. By using this condition, we compute all examples of families C → P 1 of covers with a primitive pure (1, 1) – VHS in Section 6.2, which will be listed in Section 6.3. By using the list of examples satisfying INT for n > 1 in [18], we give in Section 6.3 the complete lists of families with a primitive pure (1, n) – VHS. In Section 6.3 we give also the complete list of examples with a derived pure (1, n) - VHS, which will be verified in Section 6.4.
CITATION STYLE
Rohde, J. C. (2009). The Computation of the Hodge Group. In Lecture Notes in Mathematics (Vol. 1975, pp. 91–119). Springer Verlag. https://doi.org/10.1007/978-3-642-00639-5_6
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