Equivalences of families of stacky toric Calabi-Yau hypersurfaces

Doran, Charles F.; Favero, David; Kelly, Tyler L.

doi:10.1090/proc/14154

Cited by 5 publications

(2 citation statements)

References 33 publications

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“…This implies that Proposition 3.5 can be seen as a generalization of [42,Theorem 3.1]. See also [22] for a recent generalization of the proposition in a more general setting and in terms of derived equivalences.…”

Section: Proof Of Theoremmentioning

confidence: 87%

Families of Calabi–Yau hypersurfaces in Q-Fano toric varieties

Artebani

Comparin

Guilbot

2016

Journal de Mathématiques Pures et Appliquées

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We provide a sufficient condition for a general hypersurface in a Q-Fano toric variety to be a Calabi-Yau variety in terms of its Newton polytope. Moreover, we define a generalization of the Berglund-Hübsch-Krawitz construction in case the ambient is a Q-Fano toric variety with torsion free class group and the defining polynomial is not necessarily of Delsarte type. Finally, we introduce a duality between families of Calabi-Yau hypersurfaces which includes both Batyrev and Berglund-Hübsch-Krawitz mirror constructions. This is given in terms of a polar duality between pairs of polytopes ∆ 1 ⊆ ∆ 2 , where ∆ 1 and ∆ * 2 are canonical.{W = 0} ⊂ P(w)/G ←→ {W * = 0} ⊂ P(w * )/G * ,

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Section: Proof Of Theoremmentioning

confidence: 87%