Talk:Deligne–Mumford stack

Todo
This page needs additional material. Here is a list of links which can be used to develop this page:
 * https://math.stackexchange.com/questions/1799741/verifying-that-the-weighted-projective-space-bbbp-bbbq1-1-2-3-is-sin
 * http://math.columbia.edu/~dejong/seminar/examples-stacks.pdf
 * https://arxiv.org/pdf/1604.02441.pdf
 * https://arxiv.org/pdf/math/0003131v1.pdf
 * https://faculty.missouri.edu/~edidind/Papers/rrforDMstacks.pdf
 * https://link.springer.com/article/10.1007/s11425-015-4970-z — Preceding unsigned comment added by Username6330 (talk • contribs) 05:07, 2 November 2017 (UTC)

Page Request
There should be a page about Artin stacks as well... — Preceding unsigned comment added by Username6330 (talk • contribs) 23:46, 3 November 2017 (UTC)


 * I think the idea is that that topic is covered in "stack" since the vast majority of stacks in natural are algebraic stacks (a.k.a. Artin stacks). -- Taku (talk) 01:20, 6 November 2017 (UTC)

Sheaves on Deligne-Mumford stacks
This page should define/discuss sheaves of modules and sheaf cohomology on deligne mumford stacks. The first place to look is of course the line bundles $$\mathcal{O}_X(k)$$ for $$X$$ a weighted projective space. For example on $$\mathbb{P}(2,3)$$

\begin{align} \Gamma(\mathcal{O}(5)) &= \mathbb{C}\cdot\{xy\} \\ \Gamma(\mathcal{O}(6)) &= \mathbb{C}\cdot \{ x^3, y^2 \} \\ \Gamma(\mathcal{O}(9)) &= \mathbb{C}\cdot \{ x^3y, y^3 \} \end{align} $$ showing how the graded ring structure is preserved by the stack similar to standard projective schemes. — Preceding unsigned comment added by Username6330 (talk • contribs) 01:34, 6 November 2017 (UTC)