Tohoku Mathematical Journal
2023
June
SECOND SERIES VOL. 75, NO. 2

Tohoku Math. J.
75 (2023), 175-213

Title QUADRATIC RELATIONS BETWEEN PERIODS OF CONNECTIONS

Author Javier Fresán, Claude Sabbah and Jeng-Daw Yu

(Received May 31, 2021, revised December 6, 2021)
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.

Mathematics Subject Classification. Primary 32G20; Secondary 34M35.
Key words and phrases. Period pairing, Poincaré-Verdier duality, quadratic relation, rapid-decay homology and cohomology, moderate homology and cohomology, real blow-up, good meromorphic flat bundle.

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