Correspondences between modular Calabi–Yau fiber products

Kapustka, Michal

doi:10.1007/s00229-009-0272-5

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Cited by 3 publications

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“…Note that the precise corresponding cusp form of weight four and level 55, as conjectured in [18,Conjecture 3], can be verified by replacing one of the factors in the fiber product by a 2-isogenous elliptic surface. This construction for correspondences between Calabi-Yau threefolds was introduced in [10]. In the present situation, it exchanges the singular fibers of type I 1 and I 2 above; the new fiber product is rigid of type (3) in the notation of Proposition 3.1.…”

Section: Application To Modularitymentioning

confidence: 97%

Non-liftable Calabi–Yau spaces

Cynk

Schütt

2012

Ark. Mat.

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Section: Application To Modularitymentioning

confidence: 97%

Non-liftable Calabi–Yau spaces

Cynk

Schütt

2012

Ark. Mat.

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A Small and Non-simple Geometric Transition

Rossi

2017

Math Phys Anal Geom

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Following notation introduced in the recent paper [41], this paper is aimed to present in detail an example of a small geometric transition which is not a simple one i.e. a deformation of a conifold transition. This is realized by means of a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y. Namikawa in Remark 2.8 and Example 1.11 of [29]. The physical interest of this example is presenting a geometric transition which can't be immediately explained as a massive black hole condensation to a massless one, as described by A. Strominger [44].

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Classification of double octic Calabi–Yau threefolds with h1,2 ≤ 1 defined by an arrangement of eight planes

Cynk

Kocel-Cynk

2018

Commun. Contemp. Math.

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In this paper, we propose a combinatorial approach to study Calabi–Yau threefolds constructed as a resolution of singularities of a double covering of [Formula: see text] branched along an arrangement of eight planes. We use this description to give a complete classification of arrangements of eight planes in [Formula: see text] defining Calabi–Yau threefolds modulo projective transformation with [Formula: see text] and to derive their geometric properties (Kummer surface fibrations, automorphisms, special elements in families).

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Correspondences between modular Calabi–Yau fiber products

Cited by 3 publications

References 30 publications

Non-liftable Calabi–Yau spaces

Non-liftable Calabi–Yau spaces

A Small and Non-simple Geometric Transition

Classification of double octic Calabi–Yau threefolds with h1,2 ≤ 1 defined by an arrangement of eight planes

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