A Note on Toric Varieties Associated to Moduli Spaces

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dc.creatorUren, James J.
dc.date2008-11-28
dc.date.accessioned2026-07-07T12:06:23Z
dc.date.available2026-07-07T12:06:23Z
dc.descriptionIn 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 $Σ^g$ 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 $g \geq 3.$
dc.description7 pages, no figures, to appear in Canad. Math. Bull
dc.identifierhttps://arxiv.org/abs/0811.4728
dc.identifierhttp://arxiv.org/abs/0811.4728
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208641
dc.subjectAlgebraic Geometry
dc.subject14M25; 52B20
dc.titleA Note on Toric Varieties Associated to Moduli Spaces
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