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Automorphy of Calabi-Yau threefolds of Borcea-Voisin type over Q

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arxiv 1212.3399 v5 pith:UHMBWTK3 submitted 2012-12-14 math.NT math.AG

Automorphy of Calabi-Yau threefolds of Borcea-Voisin type over Q

Yasuhiro Goto , Ron Livne , Noriko Yui This is my paper
classification math.NT math.AG
keywords calabi-yauthreefoldsautomorphyborcea-voisinconsidermodulisurfacestype
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We consider Calabi-Yau threefolds of Borcea-Voisin type over Q. They are constructed from products of K3 surfaces and elliptic curves. We use concrete K3 surfaces and discuss the automorphy of the Galois representations associated to the Calabi-Yau threefolds. The moduli spaces of these Calabi-Yau threefolds are Shimura varieties. Our result shows the existence of a CM point in the moduli space. We also consider mirror symmetry of Calabi-Yau threefolds.

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  1. Hodge numbers for orbifolds of Calabi-Yau threefolds Ferma type and the Roan pairs

    hep-th 2026-07 reject novelty 5.0

    For all Fermat-type Calabi-Yau threefold orbifolds, a Roan-pair counting recipe is claimed to reproduce string-theoretic Euler numbers; for ten cases it matches Borcea-Voisin mirrors.