Smoothability of relative stable maps to stacky curves

Relative Compactness and Product Stable Quotient Maps

Stable Maps of Curves

Let h:X → Y be a finite morphism of smooth connected complete curves over Cp. We show h extends to a finite morphism between semi-stable models of X and Y . 2000 Mathematics Subject Classification: 11G20

relative compactness and product stable quotient maps

Stable Modification of Relative Curves

We generalize theorems of Deligne-Mumford and de Jong on semistable modifications of families of proper curves. The main result states that after a generically étale alteration of the base any (not necessarily proper) family of multipointed curves with semi-stable generic fiber admits a minimal semi-stable modification. The latter can also be characterized by the property that its geometric fib...

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...