A Note on Toric Varieties Associated to Moduli Spaces TeX Export

@article{citeulike:3733908, abstract = {In this note we give a brief review of the construction of a toric variety \$\mathcal{V}\$ coming from a genus \$g \geq 2\$ Riemann surface \$\Sigma^g\$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey in \cite{JH1}. In \cite{T1} 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 \$\mathcal{V}.\$ In particular, we show that the varieties \$DM\_g\$ constructed by Tyurin, and claimed to be smooth, are in fact singular for \$g \geq 3.\$}, archivePrefix = {arXiv}, author = {Uren, James J.}, citeulike-article-id = {3733908}, citeulike-linkout-0 = {http://arxiv.org/abs/0811.4728}, citeulike-linkout-1 = {http://arxiv.org/pdf/0811.4728}, day = {28}, eprint = {0811.4728}, keywords = {genus, surfaces, toric\_varieties}, month = {Nov}, posted-at = {2009-11-10 05:00:54}, priority = {2}, title = {A Note on Toric Varieties Associated to Moduli Spaces}, url = {http://arxiv.org/abs/0811.4728}, year = {2008} }

TY - JOUR ID - citeulike:3733908 L3 - citeulike-article-id:3733908 N2 - In this note we give a brief review of the construction of a toric variety $\mathcal{V}$ coming from a genus $g \geq 2$ Riemann surface $\Sigma^g$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey in \cite{JH1}. In \cite{T1} 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 $\mathcal{V}.$ In particular, we show that the varieties $DM_g$ constructed by Tyurin, and claimed to be smooth, are in fact singular for $g \geq 3.$ TI - A Note on Toric Varieties Associated to Moduli Spaces KW - genus KW - surfaces KW - toric_varieties AU - Uren, James PY - 2008/Nov/28/ UR - http://arxiv.org/abs/0811.4728 ER -