| 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. |