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Let $$f$$ f and $$g$$ g be holomorphic function-germs vanishing at the origin of complex analytic germs of dimension three. Suppose that they have no common irreducible component and that the real analytic map-germ $$f\bar{g}$$ f g ¯ has an isolated critical value at 0. We give necessary and sufficient conditions for the real analytic map-germ $$f\bar{g}$$ ...
By analyzing the local and infinitesimal behavior of degenerating polarized variations of Hodge structure the notion of infinitesimal variation of Hodge structure at infinity is introduced. It is shown that all such structures can be integrated to polarized variations of Hodge structure and that, conversely, all are limits of infinitesimal variations of Hodge structure at finite points. As an illustration...
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