Permutohedral spaces and the Cox ring of the moduli space of stable pointed rational curves

Details Permutohedral spaces and the Cox ring of the moduli space of stable pointed rational curves Permutohedral spaces and the Cox ring of the moduli space of stable pointed rational curves

2011-05-25

arxiv.org/abs/1105.5106v1

Mathematics

Algebraic Geometry

20 pages, 2 figures, comments welcome

Scientific paper

We study the Cox ring of the moduli space of stable pointed rational curves, \M_{0,n}, via the closely related permutohedral (or Losev-Manin) spaces. Our main result establishes \binom{n}{2} polynomial subrings of the Cox ring, thus giving collections of boundary variables that intersect the ideal of relations trivially. As applications, we give a combinatorial way to partially solve the Riemann-Roch problem for \M_{0,n}, and we show that all relations in degrees of Cox(\M_{0,6}) arising from certain pull-backs from projective spaces are generated by the Plucker relations.

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