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Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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Does Albanese construction yield a morphism to moduli of abelian varieties?

Let $M_h$ be the (coarse) moduli space of polarized manifolds with Hilbert function $h$. I would like to know if the albanese $Alb(X)$ of a polarized manifold $X$ gives rise to a morphism $M_h\to A_{g …
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