Abel Maps for nodal curves via tropical geometry

On Abel Maps of Stable Curves

We construct Abel maps for a stable curve X. Namely, for each one-parameter deformation of X to a smooth curve, having regular total space, and each integer d ≥ 1, we construct by specialization a map αdX : Ẋ d → P d X , where Ẋ ⊆ X is the smooth locus, and P d X is the moduli scheme for balanced line bundles on semistable curves over X. For d = 1, we show that αX extends to a map α 1 X : X → P...

Naturality of Abel maps

We give a combinatorial characterization of nodal curves admitting a natural (i.e. compatible with and independent of specialization) d-th Abel map for any d ≥ 1. Let X be a smooth projective curve and d a positive integer; the classical d-th Abel map of X , αX : X d −→ PicX , associates to (p1, . . . , pd) ∈ X the class of the line bundle OX(p1 + . . .+ pd) in Pic d X . Such a morphism has goo...

Geometry on Nodal Curves Ii: Cycle Map and Intersection Calculus

Cohomological Support Loci for Abel-prym Curves

For an Abel-Prym curve contained in a Prym variety, we determine the cohomological support loci of its twisted ideal sheaves and the dimension of its theta-dual.

A pr 2 00 9 Abel maps for curves of compact type

Recently, the first Abel map for a stable curve of genus g ≥ 2 has been constructed. Fix an integer d ≥ 1 and let C be a stable curve of compact type of genus g ≥ 2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the 2-n...