A closer look at the stacks of stable pointed curves (Q1936108)

In an earlier work [Math. Scand. 52, 161--199 (1983; Zbl 0544.14020)], the author constructed two functors, contraction and stabilization, in order to show that the moduli space of stable pointed genus \(g\) curves is a Deligne-Mumford stack. In the treatment of stabilization, there is a claim regarding the deformations of pointed nodes, which is not proved. The main result of the paper under review gives a proof of the claim. In addition, the author chooses to work with the Zariski topology instead of the étale topology and the descent method. As a result, the equations become less simple, but the treatment is more elementary and general.