Degeneration of torsors over families of del Pezzo surfaces

Ulrich Derenthal and Norbert Hoffmann

Mathematische Nachrichten, 2020, vol. 293, issue 12, 2306-2334

Abstract: 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.

Date: 2020
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https://doi.org/10.1002/mana.201900546

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