Tohoku Mathematical Journal
2011
December
SECOND SERIES VOL. 63, NO. 4

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

Title THE FUNCTOR OF TORIC VARIETIES ASSOCIATED WITH WEYL CHAMBERS AND LOSEV-MANIN MODULI SPACES

Author Victor Batyrev and Mark Blume

(Received July 8, 2010)
Abstract. 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 $\overline{L}_{n+1}$ of stable $(n+1)$-pointed chains of projective lines investigated by Losev and Manin.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14D22, 14H10.
Key words and phrases. Toric varieties, root systems, Losev-Manin moduli spaces.

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