Constructing new Calabi-Yau 3-folds and their mirrors via conifold transitions

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dc.creatorBatyrev, Victor
dc.creatorKreuzer, Maximilian
dc.date2008-02-22
dc.date2008-03-03
dc.date.accessioned2026-07-07T09:24:01Z
dc.date.available2026-07-07T09:24:01Z
dc.descriptionWe construct a surprisingly large class of new Calabi-Yau 3-folds $X$ with small Picard numbers and propose a construction of their mirrors $X^*$ using smoothings of toric hypersurfaces with conifold singularities. These new examples are related to the previously known ones via conifold transitions. Our results generalize the mirror construction for Calabi-Yau complete intersections in Grassmannians and flag manifolds via toric degenerations. There exist exactly 198849 reflexive 4-polytopes whose 2-faces are only triangles or parallelograms of minimal volume. Every such polytope gives rise to a family of Calabi-Yau hypersurfaces with at worst conifold singularities. Using a criterion of Namikawa we found 30241 reflexive 4-polytopes such that the corresponding Calabi-Yau hypersurfaces are smoothable by a flat deformation. In particular, we found 210 reflexive 4-polytopes defining 68 topologically different Calabi--Yau 3-folds with $h_{11}=1$. We explain the mirror construction and compute several new Picard--Fuchs operators for the respective 1-parameter families of mirror Calabi-Yau 3-folds.
dc.descriptionminor corrections
dc.identifierhttps://arxiv.org/abs/0802.3376
dc.identifierhttp://arxiv.org/abs/0802.3376
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155943
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleConstructing new Calabi-Yau 3-folds and their mirrors via conifold transitions
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