Geometry of polysymbols

Masanori Morishita; Yuji Terashima

doi:10.4310/MRL.2008.v15.n1.a9

Geometry of polysymbols

Masanori Morishita, Yuji Terashima

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	95-115
Number of pages	21
Journal	Mathematical Research Letters
Volume	15
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2008.v15.n1.a9
Publication status	Published - 2008 Jan
Externally published	Yes

Keywords

Deligne cohomology
Iterated integral
Massey product
Polysymbol

ASJC Scopus subject areas

Mathematics(all)

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10.4310/MRL.2008.v15.n1.a9

Cite this

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title = "Geometry of polysymbols",

abstract = "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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author = "Masanori Morishita and Yuji Terashima",

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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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KW - Iterated integral

KW - Massey product

KW - Polysymbol

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JO - Mathematical Research Letters

JF - Mathematical Research Letters

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Geometry of polysymbols

Abstract

Keywords

ASJC Scopus subject areas

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