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29 March 2024
 
  » arxiv » 1005.1272

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Adjoint representation of E_8 and del Pezzo surfaces of degree 1
Vera V. Serganova ; Alexei N. Skorobogatov ;
Date 7 May 2010
AbstractLet X be a del Pezzo surface of degree 1, and let G be the simple Lie group of type E_8. We construct a locally closed embedding of a universal torsor over X into the G-orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Neron-Severi torus T of X identified with a maximal torus of G extended by the group of scalars. The T-invariant hyperplane sections of the torsor defined by the roots of G are inverse images of the 240 exceptional curves on X. This extends the main result of our previous work to del Pezzo surfaces of degree 1.
Source arXiv, 1005.1272
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