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Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras

Willem A. de Graaf·Jana Pílniková·Josef Schicho
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Abstract

For a Del Pezzo surface of degree 8 given over the rationals we decide whether there is a rational parametrization of the surface and construct one in the affirmative case. We define and use the Lie algebra of the surface to reach the aim. The algorithm has been implemented in Magma.

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Willem A. de Graaf, Jana Pílniková, Josef Schicho. 2005-12-20. Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras. https://arxiv.org/abs/math/0512477

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