Zeta functions of alternate mirror Calabi–Yau families
Authors
Doran, Charles F
Kelly, Tyler
Salerno, Adriana
Sperber, Steven
Voight, John
Whitcher, Ursula
Publication Date
2018-10Journal Title
Israel Journal of Mathematics
ISSN
0021-2172
Publisher
Springer Nature
Volume
228
Issue
2
Pages
665-705
Language
en
Type
Article
This Version
VoR
Metadata
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Doran, C. F., Kelly, T., Salerno, A., Sperber, S., Voight, J., & Whitcher, U. (2018). Zeta functions of alternate mirror Calabi–Yau families. Israel Journal of Mathematics, 228 (2), 665-705. https://doi.org/10.1007/s11856-018-1783-0
Abstract
We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common factor is related to a hypergeometric Picard–Fuchs differential equation. The factor in the zeta function is defined over the rationals and has degree at least the order of the Picard–Fuchs equation. As an application, we relate several pencils of K3 surfaces to the Dwork pencil, obtaining new cases of arithmetic mirror symmetry.
Sponsorship
EPSRC (EP/N004922/1)
Embargo Lift Date
2100-01-01
Identifiers
External DOI: https://doi.org/10.1007/s11856-018-1783-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/275809