Degeneration of torsors over families of del Pezzo surfaces

AbstractLetSbe a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ‐singularities. LetGbe the reductive group given by the root system of these singularities. We construct aG‐torsor overSwhose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of Friedman and Morgan for individual singular del Pezzo surfaces. In case of very good residue characteristic, this torsor is unique and infinitesimally rigid.