Geometry of polysymbols

We introduce a multiple generalization of the tame symbol, called {\em polysymbols}, associated to meromorphic functions on a Riemann surface as the Massey products in Deligne cohomology, and also give a geometric construction of polysymbols using Chen’s iterated integrals. We then deduce some basic properties of polysymbols using our holonomy formula, and show that trivializations of polysymbols give variations of mixed Hodge structure.

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Published 1 January 2008