Tohoku Mathematical Journal

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

Victor Batyrev and Mark Blume

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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.

Article information

Tohoku Math. J. (2), Volume 63, Number 4 (2011), 581-604.

First available in Project Euclid: 6 January 2012

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Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14D22: Fine and coarse moduli spaces 14H10: Families, moduli (algebraic)

Toric varieties root systems Losev-Manin moduli spaces


Batyrev, Victor; Blume, Mark. The functor of toric varieties associated with Weyl chambers and Losev-Manin moduli spaces. Tohoku Math. J. (2) 63 (2011), no. 4, 581--604. doi:10.2748/tmj/1325886282.

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