# Contents

## Definition

$\mathbb{P}(X) := (X-\{0\})/\mathbb{G}_m$

by the action of a multiplicative group object (for a given line object).

If instead of forming the quotient one forms the weak quotient/action groupoid, one speaks of the projective stack

$\hat \mathbb{P}(X) := (X-\{0\})//\mathbb{G}_m \,.$

## References

The definition appears for instance as def 2.1.1 in

• Dan Abramovich and Brendan Hasset, Stable varieties with a twist (ps)

Created on December 28, 2010 19:55:52 by Urs Schreiber (89.204.137.67)