2014
DOI: 10.1007/s00220-014-2121-y
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Birationality of Berglund–Hübsch–Krawitz Mirrors

Abstract: ABSTRACT. We investigate a multiple mirror phenomenon arising from BerglundHübsh-Krawitz mirror symmetry. We prove that the different mirror Calabi-Yau orbifolds which arise in this context are in fact birational to one another. CONTENTS

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Cited by 20 publications
(16 citation statements)
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“…This question is answered affirmatively in many ways in the literature by Borisov [Bor13], Shoemaker [Sho14], Kelly [Kel13], and Clarke [Cla13]. In this paper, we prove that these mirrors are the same from the perspective of homological mirror symmetry.…”
Section: Introductionsupporting
confidence: 58%
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“…This question is answered affirmatively in many ways in the literature by Borisov [Bor13], Shoemaker [Sho14], Kelly [Kel13], and Clarke [Cla13]. In this paper, we prove that these mirrors are the same from the perspective of homological mirror symmetry.…”
Section: Introductionsupporting
confidence: 58%
“…There have been a few toric reinterpretations of BHK mirror duality in the literature ( [Bor13], [Cla08], [Sho14]). In this subsection, we will give a brief overview of the framework that we will use and introduce the relevant notation for the BHK mirror construction both in a Landau-Ginzburg and a Calabi-Yau setting.…”
Section: Toric Reinterpretation Of Bhk Mirrorsmentioning
confidence: 99%
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“…In [11], Shoemaker proved that BHK-mirrors of distinct Calabi-Yau orbifolds are birational provided the original Calabi-Yau's lie in the same weighted projective space and the group used to quotient them is the same. More recently, Kelly was able to prove this result assuming only that the group was the same [9]; in particular the assumption that the hypersurfaces lie in the same projective space was dropped.…”
Section: Introductionmentioning
confidence: 99%
“…For instance, it may happen that two different almost pseudoreflexive polytopes ∆ 1 = ∆ 2 have the same pseudoreflexive duals, i.e., [∆ * 1 ] = [∆ * 2 ]. This equality is the key observation for the birationality of BHK-mirrors investigated in[Ke13,Cla14,Sh14].…”
mentioning
confidence: 69%