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Special fiber of the Neron Model of an Abelian scheme in terms of Limit Hodge Structure

Let $\mathcal{A}$ be an Abelian scheme over a smooth curve $S^*\subset S$ and let $\mathcal{A_S}$ be the Neron model of $\mathcal{A}$ over $S$. Is it possible to describe the special fiber of the ...