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arXiv · 1301.2582

On some Hermitian variations of Hodge structure of Calabi-Yau type with real multiplication

Robert Friedman·Radu Laza
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Abstract

We prove that, for every totally real number field E_0, there exists a weight three variation of Hodge structure of Calabi-Yau type defined over the rational numbers with associated endomorphism algebra E_0 such that the unique irreducible factor of Calabi-Yau type of the corresponding real variation of Hodge structure is the canonical real VHS of CY type over the Hermitian symmetric domain II_6, associated to the real group SO^*(12). The main point is a rationality result for the half spin representations of a form of the group SO^*(4m) defined over a number field.

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Robert Friedman, Radu Laza. 2013-04-20. On some Hermitian variations of Hodge structure of Calabi-Yau type with real multiplication. https://arxiv.org/abs/1301.2582

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