Geometry of polysymbols

Masanori Morishita, Yuji Terashima

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)95-115
Number of pages21
JournalMathematical Research Letters
Volume15
Issue number1
DOIs
Publication statusPublished - Jan 2008

Fingerprint

Mixed Hodge Structure
Iterated integral
Holonomy
Meromorphic Function
Riemann Surface
Cohomology
Deduce
Generalization

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Geometry of polysymbols. / Morishita, Masanori; Terashima, Yuji.

In: Mathematical Research Letters, Vol. 15, No. 1, 01.2008, p. 95-115.

Research output: Contribution to journalArticle

Morishita, Masanori ; Terashima, Yuji. / Geometry of polysymbols. In: Mathematical Research Letters. 2008 ; Vol. 15, No. 1. pp. 95-115.
@article{8d2dfef0e77344ef9e55faeb6c88cbd6,
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.",
author = "Masanori Morishita and Yuji Terashima",
year = "2008",
month = "1",
doi = "10.4310/MRL.2008.v15.n1.a9",
language = "English",
volume = "15",
pages = "95--115",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "1",

}

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.

UR - http://www.scopus.com/inward/record.url?scp=41149146226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41149146226&partnerID=8YFLogxK

U2 - 10.4310/MRL.2008.v15.n1.a9

DO - 10.4310/MRL.2008.v15.n1.a9

M3 - Article

AN - SCOPUS:41149146226

VL - 15

SP - 95

EP - 115

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 1

ER -