TY - JOUR
T1 - Geometry of polysymbols
AU - Morishita, Masanori
AU - Terashima, Yuji
PY - 2008/1
Y1 - 2008/1
N2 - We introduce a multiple generalization of the tame symbol, called 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.
AB - We introduce a multiple generalization of the tame symbol, called 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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U2 - 10.4310/MRL.2008.v15.n1.a9
DO - 10.4310/MRL.2008.v15.n1.a9
M3 - Article
AN - SCOPUS:41149146226
SN - 1073-2780
VL - 15
SP - 95
EP - 115
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 1
ER -