The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces

Details The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces

2009-11-18

arxiv.org/abs/0911.3607v4

Tohoku Math. J. 63 (2011), 581-604

Mathematics

Algebraic Geometry

25 pages

Scientific paper

A root system $R$ of rank $n$ defines an $n$-dimensional smooth projective toric variety $X(R)$ associated with its fan of Weyl chambers. We give a simple description of the functor of $X(R)$ in terms of the root system $R$ and apply this result in the case of root systems of type $A$ to give a new proof of the fact that the toric variety $X(A_n)$ is the fine moduli space $\bar{L}_{n+1}$ of stable $(n+1)$-pointed chains of projective lines investigated by Losev and Manin.

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