Compactified Jacobians and Torelli Map

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TORELLI THEOREM FOR GRAPHS AND TROPICAL CURVES (2009, methodology): “nd 4.1.8). A key ingredient turns out to be the Delaunay decomposition Del(Γ) of a graph Γ. Del(Γ) is well known to be a powerful tool, and has been investigated in, among others, [Nam76], [OS79] and [Ale04], which have been quite useful in the writing of this paper. In Proposition 3.2.3, we charact”
Néron models and compactified Picard schemes over the moduli stack of stable curves (2005, background): “rees. A remarkable case is d= g−1, which has been particularly studied (partly in relation with the problem of extending the theta-divisor). Some correlation results have been proved by V. Alexeev in [Al04] where there is also an overview of the various existing constructions. As shown in 5.10, the ”
Moduli of roots of line bundles on curves (2004, result): “Recent results in [2] show that, under suitable hypotheses, the spaces of [5] and [24] coincide; other correlation results are, at least to us, not known.”
On the tropical Torelli map (2009, background): “The above map tg admits also a modular interpretation (see [2]), which was used in [10] to give a description of its fibers.”