In an exercise of Voisin book, says:

Let $j:C\rightarrow S$ the inclusion of a smooth curve on a smooth connected projective surface. Set $H=ker(j_*:H^1(C,\mathbb{Z})\rightarrow H^3(S,\mathbb{Z}))$.

We also write $A\subset J(C)$ for the Abelian subvariety corresponding to the Hodge substructure $H$.

I do not undertand how the correspondence between Abelian subvarieties and Hodge substructures goes, so I will be grateful if someone can suggest to me a reference to learn it. Thank you

In an exercise of Voisin book, says:

Let $j:C\rightarrow S$ the inclusion of a smooth curve on a smooth connected projective surface. Set $H=ker(j_*:H^1(C,\mathbb{Z})\rightarrow H^3(S,\mathbb{Z}))$.

We also write $A\subset J(C)$ for the Abelian subvariety corresponding to the Hodge substructure $H$.

I do not understand how the correspondence between Abelian subvarieties and Hodge substructures goes, so I will be grateful if someone can suggest to me a reference to learn it. Thank you