Degeneration of torsors over families of del Pezzo surfaces

Abstract

AbstractLet S be 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. Let G be the reductive group given by the root system of these singularities. We construct a G‐torsor over S whose 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.