Equivariant Gerbes I: Translations of Complex Tori

Details Equivariant Gerbes I: Translations of Complex Tori Equivariant Gerbes I: Translations of Complex Tori

2011-02-11

arxiv.org/abs/1102.2312v1

Mathematics

Algebraic Geometry

Scientific paper

We explore a new direction in representation theory which comes from holomorphic gerbes on complex tori. The analogue of the theta group of a holomorphic line bundle on a (compact) complex torus is developed for gerbes in place of line bundles. The theta group of symmetries of the gerbe has the structure of a Picard groupoid. We calculate it explicitly as a central extension of the group of symmetries of the gerbe by the Picard groupoid of the underlying complex torus. We discuss obstruction to equivariance and give an example of a group of symmetries of a gerbe with respect to which the gerbe cannot be equivariant. We survey various types of representations of the group of symmetries of a gerbe on the stack of sheaves of modules on the gerbe and the associated abelian category of sheaves on the gerbe (twisted sheaves).

Affiliated with

Also associated with

No associations

Rating

Equivariant Gerbes I: Translations of Complex Tori does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Equivariant Gerbes I: Translations of Complex Tori, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equivariant Gerbes I: Translations of Complex Tori will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-632370