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Degeneration of torsors over families of del Pezzo surfaces

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  • Ulrich Derenthal
  • Norbert Hoffmann

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.

Suggested Citation

  • Ulrich Derenthal & Norbert Hoffmann, 2020. "Degeneration of torsors over families of del Pezzo surfaces," Mathematische Nachrichten, Wiley Blackwell, vol. 293(12), pages 2306-2334, December.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:12:p:2306-2334
    DOI: 10.1002/mana.201900546
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