A remark on tube domains. (English) Zbl 0873.32032

Summary: Let \(D\) be a tube domain (i.e. a bounded symmetric domain of tube type). In Proc. Symp. Pure Math. 33, No. 2, 247-290 (1979; Zbl 0437.14012) P. Deligne gives a description of \(D\) as the moduli space of certain Hodge structures. Using these methods, we show that \(D\) parametrizes a canonical variation \({\mathcal V}\) of polarized real Hodge structures, which is effective of weight \(=\text{rank}(D)\) and enjoys several remarkable properties. We end with some speculation on how \({\mathcal V}\) might appear in algebraic geometry.


32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
32G20 Period matrices, variation of Hodge structure; degenerations
14D07 Variation of Hodge structures (algebro-geometric aspects)


Zbl 0437.14012
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