Equivariant gerbes on complex tori

JOURNAL OF GEOMETRY AND PHYSICS

卷:64

Article

Ben-Bassat, Oren

关键词: Gerbes;    Complex tori;    Heisenberg group;    Brauer group;   

DOI  :  10.1016/j.geomphys.2012.10.012

来源: Elsevier

【 摘 要 】

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 calculate the obstructions to invariant gerbes for some group of translations of a torus to 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). (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free