Holomorphic Gerbes on Complex Tori and other Varieties
Talk by Dr. Oren Ben-Bassat
Speaker invited by: Prof. Dr. Andrew Kresch
Date: 18.04.11 Time: 13.15 - 14.45 Room: Y27H25
Holomorphic gerbes are certain geometric objects whose isomorphism classes form the second cohomology group of the sheaf of nowhere vanishing holomorphic functions. Locally a gerbe on a small open set should be thought of as something isomorphic to the category of all line bundles. Actually the line bundles act on gerbes similarly to the way to functions act on line bundles. In this talk, I will give an elementary description of gerbes. In the holomorphic context, I will discuss the relationship to the topology of divisors. I will present some aspects of the study of gerbes on complex tori. This study is analogous to the classical study of line bundles on complex tori. Concepts such as the Appell-Humbert theorem, and the Poincare bundle and more will be presented in this new setting. I will discuss equivariance of gerbes on complex tori under translation action.