Abstract
Let f : C → B be a smoothing of a stable curve C and S f ∗ be the moduli space of theta characteristics on the smooth fibers of f. We describe the Néron model N ( S f ∗ ) , in terms of combinatorial invariants of the dual graph of C. Furthermore, we provide a modular description of N ( S f ∗ ) and we construct an immersion ψ f : N ( S f ∗ ) ↪ J E σ , where J E σ is a suitable relative compactified Jacobian. We show that ψ f factors through the locus of J E σ parametrizing locally free rank-1 sheaves.
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