A Note on Toric Varieties Associated with Moduli Spaces

作者：Uren James J^*

来源：Canadian Mathematical Bulletin, 2011, 54(3): 561-565.

DOI：10.4153/CMB-2010-109-4

In this note we give a brief review of the construction of a toric variety V coming from a genus g >= 2 Riemann surface Sigma(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 DM(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 V. In particular, we show that the varieties DM(g) constructed by Tyurin, and claimed to be smooth, are in fact singular for g >= 3.

• 出版日期2011-9