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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 | Abstract: | Let 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 | Services: | Forum | Review | PDF | Favorites |
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