Pfaffian Calabi–Yau threefolds and mirror symmetry

Kanazawa, Atsushi

doi:10.4310/cntp.2012.v6.n3.a3

Cited by 31 publications

(80 citation statements)

References 16 publications

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“…This model has an M -point in the ζ 0-phase which is a smooth Pfaffian CY in weighted P 7 [43] characterized by the condition rkA(p) = 2. It is a strongly coupled phase where an SU (2) subgroup of G remains unbroken.…”

Section: Non-abelian Example With a Pseudo-hybrid Phasesmentioning

confidence: 99%

Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

Erkinger

Knapp

2019

J. High Energ. Phys.

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We test the refined swampland distance conjecture in the Kähler moduli space of exotic one-parameter Calabi-Yaus. We focus on examples with pseudo-hybrid points. These points, whose properties are not well-understood, are at finite distance in the moduli space. We explicitly compute the lengths of geodesics from such points to the large volume regime and show that the refined swampland distance conjecture holds. To compute the metric we use the sphere partition function of the gauged linear sigma model. We discuss several examples in detail, including one example associated to a gauged linear sigma model with non-abelian gauge group. Refined swampland distance conjectureThe swampland distance conjecture (SDC) is a statement on the properties of the scalar moduli spaces of a consistent theory of quantum gravity. The claim is that, given a scalar moduli space M and a point p 0 ∈ M, there exist other points p ∈ M that are arbitrarily far away from p 0 . At these parametrically large distances Θ = d(p, p 0 ) an infinitely large tower of light states appears,where M 0 and M are the masses at p 0 and p, respectively. The geodesic distance Θ = d(p, p 0 ) is obtained from the metric on M. As Θ → ∞ the field theory description breaks down due to infinitely many massless degrees of freedom.

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Section: Non-abelian Example With a Pseudo-hybrid Phasesmentioning

confidence: 99%

Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

Erkinger

Knapp

2019

J. High Energ. Phys.

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“…The threefolds studied in this paper have received some attention in recent years, partly from the perspective of mirror symmetry, see [18,[20][21][22]. In particular, the question of whether the X g have non-trivial Fourier-Mukai partners was raised in [14,Remark,p.…”

Section: Other Workmentioning

confidence: 99%

“…Then X g is a simply connected smooth Calabi-Yau threefold. The non-trivial Hodge numbers of X g were computed by Kanazawa [20] to be h 1,1 (X) = 1, h 1,2 (X) = 51. The family of all X g is locally complete.…”

Section: Introductionmentioning

confidence: 99%

A counterexample to the birational Torelli problem for Calabi-Yau threefolds

Ottem

Rennemo

2018

J. London Math. Soc.

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The Grassmannian Gr(2, 5) is embedded in P 9 via the Plücker embedding. The intersection of two general PGL(10)-translates of Gr(2, 5) is a Calabi-Yau threefold X, and the intersection of the projective duals of the two translates is another Calabi-Yau threefold Y , deformation equivalent to X. Applying results of Kuznetsov and Jiang-Leung-Xie shows that X and Y are derived equivalent, which by a result of Addington implies that their third cohomology groups are isomorphic as polarised Hodge structures. We show that X and Y provide counterexamples to a certain 'birational' Torelli statement for Calabi-Yau threefolds, namely, they are deformation equivalent, derived equivalent, and have isomorphic Hodge structures, but they are not birational.Proposition 1.1. Let g ∈ PGL(∧ 2 V ) be such that X g and Y g are of expected dimension. Then we have an equivalence of derived categories

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“…The dimension of the graded component we get in return is 1,10,22,11,1 where we have to look at the component of degree 1, since (T 1 [4] and [26]. We define…”

Section: Let Us Produce a Code In Singularmentioning

confidence: 99%

Hodge theory and deformations of affine cones of subcanonical projective varieties

Natale¹,

Fatighenti

Fiorenza

2017

J. London Math. Soc.

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Abstract. We investigate the relation between the Hodge theory of a smooth subcanonical n-dimensional projective variety X and the deformation theory of the affine cone AX over X. We start by identifying H n−1,1 prim (X) as a distinguished graded component of the module of first order deformations of AX, and later on we show how to identify the whole primitive cohomology of X as a distinguished graded component of the Hochschild cohomology module of the punctured affine cone over X. In the particular case of a projective smooth hypersurface X we recover Griffiths' isomorphism between the primitive cohomology of X and certain distinguished graded components of the Milnor algebra of a polynomial defining X. The main result of the article can be effectively exploited to compute Hodge numbers of smooth subcanonical projective varieties. We provide a few example computation, as well a SINGULAR code, for Fano and Calabi-Yau threefolds.

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Pfaffian Calabi–Yau threefolds and mirror symmetry

Cited by 31 publications

References 16 publications

Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

A counterexample to the birational Torelli problem for Calabi-Yau threefolds

Hodge theory and deformations of affine cones of subcanonical projective varieties

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