Abstract
Let Xr be a smooth Del Pezzo surface obtained from ℙ(2 by blowing up r ⩽8 points in general position. It is well known that for r ε {3,4,5,6,7,8} the Picard group Pic(X r ) contains a canonical root system R r € A 2 × A1, A4, D5, E6, E7, E8. We prove some general properties of the Cox ring of X r (r ⩾ 4) and show its similarity to the homogeneous coordinate ring of the orbit of the highest weight vector in some irreducible representation of the algebraic group G associated with the root system R r .
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Batyrev, V.V., Popov, O.N. (2004). The Cox Ring of a Del Pezzo Surface. In: Poonen, B., Tschinkel, Y. (eds) Arithmetic of Higher-Dimensional Algebraic Varieties. Progress in Mathematics, vol 226. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8170-8_5
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DOI: https://doi.org/10.1007/978-0-8176-8170-8_5
Publisher Name: Birkhäuser, Boston, MA
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