5
$\begingroup$

I am looking for a good reference (if there is any) for the theory of orbifold curves from the perspective of stacks. By an orbifold curve I mean something like a $1$-dimensional irreducible Deligne-Mumford stack $\mathcal{X}$ with generically trivial stabilizers. Mostly, I am interested in their categories of coherent sheaves (derived and abelian).

In spite of the fact that these objects are fairly concrete, I haven't seen too many references in the literature that collect results about them and I'd really appreciate a citeable reference to avoid having to reprove things that are probably well-known.

Improve this question
$\endgroup$

2 Answers 2

Reset to default
4
$\begingroup$

The answer to your question is that there is no good reference.

I am finishing up my PhD thesis on moduli of sheaves on stacky curves. If you want I can send you some drafts, that will hopefully be good citeable references in the future.

Improve this answer
$\endgroup$
1
  • $\begingroup$ Dear Lisanne, Thanks for the offer. It would, of course, be appreciated. You can find my email on my personal page linked in my profile. Thanks in advance. $\endgroup$
    – Alekos Robotis
    Commented May 30 at 21:15
4
$\begingroup$

John Voight and I have a chapter in our book which collects proofs of several "well known" facts about stacky curves (e.g., the formula for the canonical divisor).

https://arxiv.org/abs/1501.04657

There we mostly only addressed facts that we needed for the rest of the book. In particular, we only work over fields. In a different paper with Ellenberg and Satriano, we needed to work with "stacky Spec Z"'s, and added some additional facts to our appendix.

https://arxiv.org/abs/2106.11340

Improve this answer
$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .