Gonality for stable curves and their maps with a smooth curve as their target

摘要

Here we study the deformation theory of some maps f : X -> P-r, r = 1, 2, where X is a nodal curve and f vertical bar T is not constant for every irreducible component T of X. For r = 1 we show that the "stratification by gonality" for any subset of (M) over bar (g)M-g with fixed topological type behaves like the stratification by gonality of M-g.