Let 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 ADE-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.

中文翻译：

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del Pezzo 表面家族上的扭力退化

令 S 是离散评估环上的 del Pezzo 曲面的分裂族，使得一般纤维是光滑的，而特殊纤维具有 ADE 奇点。令 G 为由这些奇点的根系统给出的约简群。我们在 S 上构造一个 G-torsor，它对通用纤维的限制是通用 Torsor 的结构群的扩展。这扩展了 Friedman 和 Morgan 对单个奇异 del Pezzo 曲面的构造。在非常好的残留特性的情况下，这个torsor是独一无二的，并且具有无限小的刚性。