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arXiv · 1601.00685

Degeneration of torsors over families of del Pezzo surfaces

Ulrich Derenthal·Norbert Hoffmann
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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.

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Ulrich Derenthal, Norbert Hoffmann. 2016-01-04. Degeneration of torsors over families of del Pezzo surfaces. https://arxiv.org/abs/1601.00685

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