QUADRATIC RELATIONS BETWEEN PERIODS OF CONNECTIONS

Javier Fresán; Claude Sabbah; Jeng Daw Yu

doi:10.2748/tmj.20211209

QUADRATIC RELATIONS BETWEEN PERIODS OF CONNECTIONS

Javier Fresán
, Claude Sabbah
, Jeng Daw Yu

Institut Polytechnique de Paris
National Taiwan University

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

Abstract

We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of “goodness”. In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we recall some classical results needed for the proofs.

Original language	English
Pages (from-to)	175-213
Number of pages	39
Journal	Tohoku Mathematical Journal
Volume	75
Issue number	2
DOIs	https://doi.org/10.2748/tmj.20211209
Publication status	Published - 1 Jan 2023

Keywords

Period pairing
Poincaré-Verdier duality
good meromorphic flat bundle
moderate homology and cohomology
quadratic relation
rapid-decay homology and cohomology
real blow-up

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10.2748/tmj.20211209

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abstract = "We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of “goodness”. In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we recall some classical results needed for the proofs.",

keywords = "Period pairing, Poincar{\'e}-Verdier duality, good meromorphic flat bundle, moderate homology and cohomology, quadratic relation, rapid-decay homology and cohomology, real blow-up",

author = "Javier Fres{\'a}n and Claude Sabbah and Yu, \{Jeng Daw\}",

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AB - We prove the existence of quadratic relations between periods of meromorphic flat bundles on complex manifolds with poles along a divisor with normal crossings under the assumption of “goodness”. In dimension one, for which goodness is always satisfied, we provide methods to compute the various pairings involved. In an appendix, we recall some classical results needed for the proofs.

KW - Period pairing

KW - Poincaré-Verdier duality

KW - good meromorphic flat bundle

KW - moderate homology and cohomology

KW - quadratic relation

KW - rapid-decay homology and cohomology

KW - real blow-up

U2 - 10.2748/tmj.20211209

DO - 10.2748/tmj.20211209

M3 - Article

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VL - 75

SP - 175

EP - 213

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

IS - 2

ER -

QUADRATIC RELATIONS BETWEEN PERIODS OF CONNECTIONS

Abstract

Keywords

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