nLab
projective stack

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Definition

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 \,.

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)