Subsection 112.5.13 (04V8): Taking roots of line bundles

112.5.13 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]

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The Stacks project

112.5.13 Taking roots of line bundles

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