Gerbes and the holomorphic Brauer group of complex tori (Q446420)

Line bundles are very important objects in mathematics. Gerbes are ``higher line bundles'', the study of which was begun by Giraud and has found applications in many places, for example, certain mathematics motivated by quantum field theory and string/M theory. The importance of gerbes in higher geometry is obvious.NEWLINENEWLINEThe study of line bundles on complex tori and the associated theta functions has rich and deep results. The author of this paper develops results for gerbes on complex tori analogous to those for line bundles on complex tori. The Appell-Humbert theorem, which selects a canonical line bundle for each isomorphism class of line bundles on complex tori, is generalized to gerbes. The author also constructs fine moduli for gerbes on complex tori. To do so, a Poincaré sheaf, a universal gerbe parameterizing topologically trivial gerbes, is constructed parallel to the story of Poincaré line bundles and moduli of line bundles.