Geodesic
A Note on Toric Varieties Associated with Moduli Spaces
Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 561-565

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DOI

In this note we give a brief review of the construction of a toric variety $\mathcal{V}$ coming from a genus $g\,\ge \,2$ Riemann surface ${{\sum }^{g}}$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety $D{{M}_{g,}}$ the so-called Delzant model of moduli space, for each genus $g$ . We conclude this note with some basic facts about the moment polytopes of the varieties $\mathcal{V}$ . In particular, we show that the varieties $D{{M}_{g}}$ constructed by Tyurin, and claimed to be smooth, are in fact singular for $g\,\ge \,3$ .
DOI : 10.4153/CMB-2010-109-4
Mots-clés : 14M25, 52B20 
Uren, James J. A Note on Toric Varieties Associated with Moduli Spaces. Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 561-565. doi: 10.4153/CMB-2010-109-4
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     title = {A {Note} on {Toric} {Varieties} {Associated} with {Moduli} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {561--565},
     year = {2011},
     volume = {54},
     number = {3},
     doi = {10.4153/CMB-2010-109-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-109-4/}
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