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On period maps that are open embeddings

Eduard Looijenga·Rogier Swierstra
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Abstract

For certain complex projective manifolds (such as K3 surfaces and their higher dimensional analogues, the complex symplectic projective manifolds) the period map takes values in a locally symmetric variety of type IV. It is often an open embedding and in such cases it has been observed that the image is the complement of a locally symmetric (Heegner) divisor. We explain that phenomenon and get our hands on the complementary divisor in terms of geometric data.

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Eduard Looijenga, Rogier Swierstra. 2005-12-21. On period maps that are open embeddings. https://arxiv.org/abs/math/0512489

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