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AN ALGORITHM OF COMPUTING COHOMOLOGY INTERSECTION NUMBER OF HYPERGEOMETRIC INTEGRALS

Part of: Algorithms - Computer Science Computational aspects

Published online by Cambridge University Press:  07 May 2021

SAIEI-JAEYEONG MATSUBARA-HEO Open the ORCID record for SAIEI-JAEYEONG MATSUBARA-HEO [Opens in a new window]  and
NOBUKI TAKAYAMA Open the ORCID record for NOBUKI TAKAYAMA [Opens in a new window]
SAIEI-JAEYEONG MATSUBARA-HEO*
Affiliation:
Graduate School of Science Kobe University 1-1 Rokkodai, Nada-ku Kobe 657-8501 Japan
NOBUKI TAKAYAMA
Affiliation:
Graduate School of Science Kobe University 1-1 Rokkodai, Nada-ku Kobe 657-8501 Japantakayama@math.kobe-u.ac.jp
*
saiei@math.kobe-u.ac.jp
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Abstract

We show that the cohomology intersection number of a twisted Gauss–Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic relation associated to period integrals of a certain family of K3 surfaces.

MSC classification

Primary: 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)
Secondary: 33C70: Other hypergeometric functions and integrals in several variables 33F99: None of the above, but in this section 68W30: Symbolic computation and algebraic computation
Type
Article
Information
Nagoya Mathematical Journal , Volume 246 , June 2022 , pp. 256 - 272
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Copyright
© 2021 The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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