Answer by NWMT for What is the official definition of $\mathcal{M}_g$ as an...
Not being a moduli space expert, I will give an answer to the more general question. To me an orbifold is a way to recover the action of a group $G$ on a space $X$ in terms of the quotient object...
View ArticleAnswer by Donu Arapura for What is the official definition of $\mathcal{M}_g$...
Since you seem to be mainly interested in $\mathcal{M_g}$, let me suggest a "quick and dirty" approach based on the following fact:$\mathcal{M}_g$ is quotient of a nonsingular algebraic variety $\tilde...
View ArticleAnswer by Sean Lawton for What is the official definition of $\mathcal{M}_g$...
Since in the comments you seem drawn to the "charts" approach to orbifolds, here are some resources which give definitions and more (there is no "official definition" as far as I know):Joan Porti has...
View ArticleWhat is the official definition of $\mathcal{M}_g$ as an orbifold, and how...
There is a well-known description of $\mathcal{M}_g$ as $\mathcal{T}_g/\Gamma$ where $\mathcal{T}_g$ is the Teichmuller space and $\Gamma$ is the mapping class group. Teichmuller space is homeomorphic...
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