2017
DOI: 10.1007/s00229-017-0936-5
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Lattice duality for families of K3 surfaces associated to transpose duality

Abstract: We study a relation between coupling introduced in [5] and the polytope duality among families of K3 surfaces.

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Cited by 6 publications
(6 citation statements)
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“…We have seen that the sum of Picard numbers ρ∆ 3 and ρ ∆ * 3 coincides with the rank of the unimodular lattice U ⊕2 ⊕E ⊕2 8 , and that the rank of L0(∆3) is 0 means that the toric 3-fold P∆ 3 is simplicial. In [13], it is concluded that if a toric Fano 3-fold P∆ is simplicial, then, the family F∆ of K3 surfaces is lattice dual in the sense that…”
Section: Remarkmentioning
confidence: 99%
“…We have seen that the sum of Picard numbers ρ∆ 3 and ρ ∆ * 3 coincides with the rank of the unimodular lattice U ⊕2 ⊕E ⊕2 8 , and that the rank of L0(∆3) is 0 means that the toric 3-fold P∆ 3 is simplicial. In [13], it is concluded that if a toric Fano 3-fold P∆ is simplicial, then, the family F∆ of K3 surfaces is lattice dual in the sense that…”
Section: Remarkmentioning
confidence: 99%
“…In [Mas16a,Mas16b,Mas17], the first author studied the Dolgachev-Nikulin-Pinkham mirror symmetry construction for K3 surfaces obtained from bimodal singularities using an invertible polynomial in four variables.…”
Section: Introductionmentioning
confidence: 99%
“…We are interested in lattice-duality originally studied by Dolgachev (1996). It is concluded by Mase (2015Mase ( , 2017) that a part of transpose-dual pairs associated to strange duality of bimodal singularities extends to lattice dual, and that some subfamilies of K 3 surfaces that are double covering of the projective plane have lattice-dual property as is studied in Mase (2021). In this paper, focusing on polytope-dual pairs associated to coupling, one may pose the following problem.…”
Section: Introductionmentioning
confidence: 99%