All Questions
Tagged with picard-group moduli-spaces
7 questions
15
votes
2
answers
3k
views
Picard Groups of Moduli Problems
First, yes, I've seen Mumford's paper of this title. I'm actually interested in specific ones, and looking for really the most elementary/elegant proof possible.
I'm told that for $g\geq 2$ it is ...
- 16k
9
votes
2
answers
839
views
$Pic$ of the stack of elliptic curves vs. $Pic$ of the coarse space
There's a natural map $f:\overline{\mathcal{M}}_{1,1}\to \overline{M}_{1,1}\cong \mathbb{P}^1$ from the stack of elliptic curves to the coarse space. Both spaces have $Pic=\mathbb{Z}$ hence $f^*:\...
- 3,779
7
votes
1
answer
543
views
Picard group of $\mathcal{M}_{0,n}$
Let $\mathcal{M}_{0,n}$ be the complement of the boundary of the Mumford-Knudsen compactification of the moduli space of genus zero, n-pointed curves.
Is $Pic(\mathcal{M}_{0,n})$ trivial?
- 3,779
3
votes
1
answer
412
views
$\psi$ class in $\overline{M}_{0,n}$
Basic question, but I found no reference.
Is the $\psi$ class the only one which is not a boundary class in the PIcard group of the Deligne-Mumford compactification of $\mathcal{M}_{0,n}$? Or can it ...
- 3,779
3
votes
0
answers
225
views
How can one check that two line bundles on $\overline{M}_{0,n}$ coincide?
Let $X$ be the Deligne-Mumford compactification of $\mathcal{M}_{0,n}$. Suppose I have two (big) line bundles $L$ and $L'$ on $X$ and that I want to show that they are the same element of $Pic(X)$. Of ...
- 3,779
2
votes
1
answer
226
views
Picard group of moduli of principal bundles
I am looking for the Picard group of the moduli space of principal $G$-bundles for a connected reductive complex algebraic group $G$.
Is it isomorphic to $\mathbb{Z}$? If not, what can we say when $G=\...
- 195
1
vote
1
answer
145
views
divisors on $\overline{\mathcal{M}}_{g,n}$ that are trivial on certain $F$-curves
Inside the moduli space of curves $\overline{\mathcal{M}}_{g,n}$ one can distinguish two classes of $F$-curves isomorphic to $\mathbb{P}^1$: those of type $\overline{\mathcal{M}}_{0,4}$, and those of ...
- 3,779