nLab projective stack




A projective space is a quotient

(X):=(X{0})/𝔾 m \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

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


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 at 19:55:53. See the history of this page for a list of all contributions to it.