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April, 2021 BHK mirror symmetry for K3 surfaces with non-symplectic automorphism
Paola COMPARIN, Nathan PRIDDIS
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J. Math. Soc. Japan 73(2): 403-431 (April, 2021). DOI: 10.2969/jmsj/79867986

Abstract

In this paper we consider the class of K3 surfaces defined as hypersurfaces in weighted projective space, that admit a non-symplectic automorphism of non-prime order, excluding the orders 4, 8, and 12. We show that on these surfaces the Berglund–Hübsch–Krawitz mirror construction and mirror symmetry for lattice polarized K3 surfaces constructed by Dolgachev agree; that is, both versions of mirror symmetry define the same mirror K3 surface.

Funding Statement

The first author has been partially supported by Proyecto Fondecyt Postdoctorado N. 3150015, Proyecto Fondecyt Iniciación en Investigación N. 11190428 and Proyecto Anillo ACT 1415 PIA Conicyt.

Citation

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Paola COMPARIN. Nathan PRIDDIS. "BHK mirror symmetry for K3 surfaces with non-symplectic automorphism." J. Math. Soc. Japan 73 (2) 403 - 431, April, 2021. https://doi.org/10.2969/jmsj/79867986

Information

Received: 14 February 2018; Revised: 29 October 2019; Published: April, 2021
First available in Project Euclid: 25 June 2020

Digital Object Identifier: 10.2969/jmsj/79867986

Subjects:
Primary: 14J28
Secondary: 11E12, 14J17, 14J32, 14J33

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 2 • April, 2021
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