The Stacks project

111.5.13 Taking roots of line bundles

This useful construction was discovered independently by Cadman and by Abramovich, Graber and Vistoli. Given a scheme $X$ with an effective Cartier divisor $D$, the $r$th root stack is an Artin stack branched over $X$ at $D$ with a $\mu _ r$ stabilizer over $D$ and scheme-like away from $D$.

  • Charles Cadman Using Stacks to Impose Tangency Conditions on Curves [cadman]

  • Abramovich, Graber, Vistoli: Gromov-Witten theory for Deligne-Mumford stacks [agv]


Comments (0)

There are also:

  • 4 comment(s) on Section 111.5: Papers in the literature

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 04V8. Beware of the difference between the letter 'O' and the digit '0'.