A mirror duality for families of \(K3\) surfaces associated to bimodular singularities
type: Item
instance of: scholarly article
title: A mirror duality for families of \(K3\) surfaces associated to bimodular singularities
zbMATH Open document ID: 1332.14042
author: Makiko Mase
published in: Manuscripta Mathematica
publication date: 2016-03-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/1702.00107
review text: \textit{M. Mase} and \textit{K. Ueda} [Manuscr. Math. 146, No. 1--2, 153--177 (2015; Zbl 1405.14104)] proved the polytope mirror symmetry for families of \(K3\) surfaces associated to bimodular singularites. In this article, the author tries to extend the polytope mirror symmetry to lattice mirror symmetry of \(K3\) surfaces in the sense of \textit{I. V. Dolgachev} [J. Math. Sci., New York 81, No. 3, 2599--2630 (1996; Zbl 0890.14024)]. The main result is that for six specific polytope mirror pairs, the lattice mirror symmetry holds. The Picard number takes values in the set \(\{2,3,4\}\). This method used in the proof is to give relations between toric geometry and lattice theory, in particular, via the intersection matrices of toric divisors and lattices.
reviewed by: Noriko Yui
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14C22
zbMATH DE Number: 6548567
zbMATH Keywords: bimodular singularites
zbMATH Keywords: polytope mirror symmetry
zbMATH Keywords: toric geometry
zbMATH Keywords: lattice mirror symmetry
zbMATH Keywords: families of K3 surfaces
zbMATH Keywords: lattice theory
MaRDI profile type: Publication
OpenAlex ID: W3102600233
arXiv ID: 1702.00107
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DOI: 10.1007/S00229-015-0788-9
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description: scientific article; zbMATH DE number 6548567