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Search: MSC category 32M15 ( Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15] )

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1. CMB Online first

Zhang, Zheng
 On motivic realizations of the canonical Hermitian variations of Hodge structure of Calabi-Yau type over type $D^{\mathbb H}$ domains Let $\mathcal{D}$ be the irreducible Hermitian symmetric domain of type $D_{2n}^{\mathbb{H}}$. There exists a canonical Hermitian variation of real Hodge structure $\mathcal{V}_{\mathbb{R}}$ of Calabi-Yau type over $\mathcal{D}$. This short note concerns the problem of giving motivic realizations for $\mathcal{V}_{\mathbb{R}}$. Namely, we specify a descent of $\mathcal{V}_{\mathbb{R}}$ from $\mathbb{R}$ to $\mathbb{Q}$ and ask whether the $\mathbb{Q}$-descent of $\mathcal{V}_{\mathbb{R}}$ can be realized as sub-variation of rational Hodge structure of those coming from families of algebraic varieties. When $n=2$, we give a motivic realization for $\mathcal{V}_{\mathbb{R}}$. When $n \geq 3$, we show that the unique irreducible factor of Calabi-Yau type in $\mathrm{Sym}^2 \mathcal{V}_{\mathbb{R}}$ can be realized motivically. Keywords:variations of Hodge structure, Hermitian symmetric domainCategories:14D07, 32G20, 32M15

2. CMB 2011 (vol 55 pp. 329)

Kamiya, Shigeyasu; Parker, John R.; Thompson, James M.
 Non-Discrete Complex Hyperbolic Triangle Groups of Type $(n,n, \infty;k)$ A complex hyperbolic triangle group is a group generated by three involutions fixing complex lines in complex hyperbolic space. Our purpose in this paper is to improve a previous result and to discuss discreteness of complex hyperbolic triangle groups of type $(n,n,\infty;k)$. Keywords:complex hyperbolic triangle groupCategories:51M10, 32M15, 53C55, 53C35
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