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Completing the web of \(\mathbb Z_3\)-quotients of complete intersection Calabi-Yau manifolds. (English) Zbl 1243.81147
Summary: We complete the study of the first author and Rh. Davies [Fortschr. Phys. 58, No. 4–5, 383–466 (2010; Zbl 1194.14062)] of smooth \(\mathbb Z_{3}\)-quotients of complete intersection Calabi-Yau threefolds by discussing the six new manifolds that admit free \(\mathbb Z_{3}\) actions that were discovered by V. Braun [“On free quotients of complete intersection Calabi-Yau manifolds”, arXiv:1003.3235]. These manifolds were missed in [Zbl 1194.14062] and complete the web of smooth \(\mathbb Z_{3}\)-quotients in a nice way. We discuss the transitions between these manifolds and include also the other manifolds of the web. This leads to the conclusion that the web of \(\mathbb Z_{3}\)-free quotients of complete intersection Calabi-Yau threefolds is connected by conifold transitions.

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
Full Text: DOI arXiv
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