Abel maps for families of curves
Eduardo Esteves (IMPA, Rio de Janeiro)

Recently, Caporaso and I have constructed degree-1 Abel maps for stable curves, or generic one-parameter smoothings of stable curves.
In this talk I will show how to extend the construction to any family of stable curves. If time allows, I will compare the two different approaches to compactifying (relative) Jacobians, by line bundles on quasistable curves or by torsion-free, rank-1 sheaves on stable curves. 

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