An equivariant line bundle is a line bundle equipped with a linearization of a group action on its base:
the action lifts to the total space and is linear
on each fiber. Tensoring the lift by a group character
can change which global sections are invariant. For an action on a smooth
variety, the differential supplies the natural linearization of 
.
Equivariant Line Bundle
See also
Anticanonical Bundle, Equivariant Euler Characteristic, Group Character, Line BundleExplore with Wolfram|Alpha
References
Milne, J. S. Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field. Cambridge, England: Cambridge University Press, 2017. https://doi.org/10.1017/9781316711736.Cite this as:
Weisstein, Eric W. "Equivariant Line Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EquivariantLineBundle.html