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MR1290721 (96c:32024) 32G20 (14C30 14D07 32J25)
Kasparian, Azniv The variations of Hodge structure of maximal dimension with associated Hodge numbers $h\sp {2,0}>2$ and $h\sp {1,1}=2q+1$ do not arise from geometry. Trans. Amer. Math. Soc. 347 (1995), no. 12, 4985–5007.
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