University of Toronto's Symplectic Geometry Seminar

May 28, 2007, 3:10pm
BA 6183

Chenchang Zhu

Institut Fourier Grenoble

A gerbe of Gamma functions---with fantasy towards toric varieties?

Abstract: As we know that theta function provides a section of a non-trivial line bundle (theta bundle) on an elliptic curve, in this talk, we will give a geometric realization of elliptic Gamma functions whose highly non-trivial identities are developed by Felder and Varchenko. Elliptic gamma function can also be regarded as the difference of theta functions. It turns out these identities can be geometrically interpreted as the fact that Gamma functions give a meremorphic section of a holomorphic gerbe over the stack [CP^2-RP^2/SL(3,Z)\times Z^3]. In the construction, a choice of frames of an integer lattice is involved. Therefore that leads some fantasy towards toric varieties...