Calabi-Yau threefolds of type K (I): Classification

Hashimoto, Kenji; Kanazawa, Atsushi

doi:10.48550/arxiv.1409.7601

Cited by 6 publications

(23 citation statements)

References 19 publications

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“…Section 2 sets conventions and recalls some basics of lattices and K3 surfaces. Section 3 begins with a brief review of the classification [16] of Calabi-Yau threefolds of type K and then investigates their topological properties, in particular their Brauer groups. Section 4 is devoted to the study of mirror symmetry, probing the A-and B-Yukawa couplings.…”

Section: Structure Of Papermentioning

confidence: 99%

“…In [16], we also obtain explicit presentations of the eight Calabi-Yau threefolds of type K. Although Calabi-Yau threefolds of type K are very special, their explicit nature makes them an exceptionally good laboratory for general theories and conjectures. Indeed, the simplest example, known as the Enriques Calabi-Yau threefold, has been one of the most tractable compact Calabi-Yau threefolds (for example [10,19]).…”

Section: Introductionmentioning

confidence: 97%

“…The importance of this class of Calabi-Yau threefolds comes from the fact that it is one of the two classes of Calabi-Yau threefolds with infinite fundamental group. In our previous work [16], based on Oguiso-Sakurai's fundamental work, we have given the full classification of Calabi-Yau threefolds of type K.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.1 ( [24,16]). There exist exactly eight Calabi-Yau threefolds of type K, up to deformation equivalence.…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Calabi–Yau threefolds of type K (II): mirror symmetry

Hashimoto

Kanazawa

2016

Communications in Number Theory and Physics

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A Calabi-Yau threefold is called of type K if it admits anétale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper [16], based on Oguiso-Sakurai's fundamental work [24], we have provided the full classification of Calabi-Yau threefolds of type K and have studied some basic properties thereof. In the present paper, we continue the study, investigating them from the viewpoint of mirror symmetry. It is shown that mirror symmetry relies on duality of certain sublattices in the second cohomology of the K3 surface appearing in the minimal splitting covering. The duality may be thought of as a version of the lattice duality of the anti-symplectic involution on K3 surfaces discovered by Nikulin [23]. Based on the duality, we obtain several results parallel to what is known for Borcea-Voisin threefolds. Along the way, we also investigate the Brauer groups of Calabi-Yau threefolds of type K.

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Section: Structure Of Papermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

“…Theorem 1.1 ( [24,16]). There exist exactly eight Calabi-Yau threefolds of type K, up to deformation equivalence.…”

Section: Introductionmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Calabi–Yau threefolds of type K (II): mirror symmetry

Hashimoto

Kanazawa

2016

Communications in Number Theory and Physics

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Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

Braun¹,

Cvetič

Donagi

et al. 2017

J. High Energ. Phys.

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Abstract:We provide the first explicit example of Type IIB string theory compactification on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z 2 × Z 2 . Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.

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Topological and Hodge L-classes of singular covering spaces and varieties with trivial canonical class

Banagl

2018

Geom Dedicata

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The signature of closed oriented manifolds is well-known to be multiplicative under finite covers. This fails for Poincaré complexes as examples of C. T. C. Wall show. We establish the multiplicativity of the signature, and more generally, the topological L-class, for closed oriented stratified pseudomanifolds that can be equipped with a middle-perverse Verdier self-dual complex of sheaves, determined by Lagrangian sheaves along strata of odd codimension (so-called L-pseudomanifolds). This class of spaces contains all Witt spaces and thus all pure-dimensional complex algebraic varieties. We apply this result in proving the Brasselet-Schürmann-Yokura conjecture for normal complex projective 3-folds with at most canonical singularities, trivial canonical class and positive irregularity. The conjecture asserts the equality of topological and Hodge L-class for compact complex algebraic rational homology manifolds.

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Calabi-Yau threefolds of type K (I): Classification

Cited by 6 publications

References 19 publications

Calabi–Yau threefolds of type K (II): mirror symmetry

Calabi–Yau threefolds of type K (II): mirror symmetry

Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

Topological and Hodge L-classes of singular covering spaces and varieties with trivial canonical class

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