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Gorenstein models of del Pezzo surfaces of degree 1 over Dedekind schemes

Mikhail Grinenko
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Abstract

Let R be a Dedekind scheme, $\nu$ its generic point, X and V del Pezzo surfaces of degree 1 over R that are Gorenstein Mori fiber spaces (as 3-folds germs over the ground field). We study birational maps $\phi:X\dasharrow V$ over R which are isomorphisms over the generic point of R. We put down normal forms of such transformations (in suitable coordinates) and give some properties of X and V. In particular, we prove the uniqueness of a smooth model.

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Mikhail Grinenko. 2000-03-24. Gorenstein models of del Pezzo surfaces of degree 1 over Dedekind schemes. https://arxiv.org/abs/math/0003153

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