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| Berzürcheley Symplectic Geometry Seminar
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| 5 Evans |
04:10 PM - 05:00 PM
03/17/2006 |
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Chenchang Zhu, ETH Zürich
A gerbe for the elliptic gamma function
As we know, the Jacobi theta function provides a section of a line bundle L with c1 = 1 on an elliptic curve T = C/Z2. The elliptic gamma function, introduced by Ruijsenaars and further studied by Felder and Varchenko, is the meromorphic solution of a first order difference equation involving the Jacobi theta function. What is the geometric interpretation of the elliptic gamma function? It turns out that it provides a section of a gerbe ˇG over the stack of universal triptic curves (a single triptic curve is C/Z3). In groupoid language, a gerbe is a central extension of groupoids. Then this gerbe ˇG restricted to a single triptic curve with groupoid presentation T × Z ⇒ T is presented by the groupoid sqcup Ln ⇒ T.
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