7
$\begingroup$

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?

$\endgroup$

1 Answer 1

12
$\begingroup$

Yes. By fixing the three points $\{0,1,\infty\}$ one sees that $M_{0,n}$ is isomorphic to an open subscheme of $\mathbb{A}^{n-3}$ which has trivial Picard group. Since it is smooth, the Picard group of any open subscheme is also trivial.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.