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Del Pezzo surfaces over Dedekind schemes

Alessio Corti
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Abstract

Let S be a Dedekind scheme with fraction field K. We study the following problem: given a Del Pezzo surface X, defined over K, construct a distinguished integral model of X, defined over all of S. We provide a satisfactory answer if S is a smooth complex curve, and a conjectural answer if X is a cubic Del Pezzo surface over (nearly) arbitrary S.

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Alessio Corti. 1995-05-31. Del Pezzo surfaces over Dedekind schemes. https://arxiv.org/abs/alg-geom/9505036

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