Lattice duality for families of K3 surfaces associated to transpose duality

Mase, Makiko

doi:10.1007/s00229-017-0936-5

Cited by 6 publications

(6 citation statements)

References 16 publications

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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%

Families of $K3$ surfaces and curves of (2,3)-torus type

Mase¹

2019

Kodai Math. J.

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We study families of K3 surfaces obtained by double covering of the projective plane branching along curves of (2, 3)-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the second part, we describe a deformation of singularities of Gorenstein K3 surfaces in these families.Running head. Families of K3 surfaces and curves of (2, 3)-torus type * Tokyo Metropolitan University and University of Mannheim, mtmase@arion.ocn.ne.jp † Keywords and phrases. families of K3 surfaces that are double cover of the projective plane, curves of (2, 3)-torus type, duality of Picard lattices, non-Galois triple covering of the projective plane ‡

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Section: Remarkmentioning

confidence: 99%

Families of $K3$ surfaces and curves of (2,3)-torus type

Mase¹

2019

Kodai Math. J.

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“…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%

Mirror constructions for K3 surfaces from bimodal singularities

Mase¹,

Whitcher²

2022

Preprint

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“…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%