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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.

MSC:
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
Software:
Mathematica
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References:
[1] Candelas, Fortschr. Phys. 58 pp 383– (2010) · Zbl 1194.14062 · doi:10.1002/prop.200900105
[2] V. Braun
[3] Candelas, Nucl. Phys. B 258 pp 46– (1985) · doi:10.1016/0550-3213(85)90602-9
[4] S.-T. Yau G. Tian S.-T. Yau 1
[5] Candelas, Adv. Theor. Math. Phys. 12 pp 429– (2008) · Zbl 1144.81499 · doi:10.4310/ATMP.2008.v12.n2.a6
[6] Candelas, Nucl. Phys. B 298 pp 493– (1988) · doi:10.1016/0550-3213(88)90352-5
[7] Braun, Fortschr. Phys. 58 pp 467– (2010) · Zbl 1194.14061 · doi:10.1002/prop.200900106
[8] T. Hübsch
[9] Bouchard, Commun. Numb. Theor. Phys. 2 pp 1– (2008) · Zbl 1165.14032 · doi:10.4310/CNTP.2008.v2.n1.a1
[12] Green, Commun. Math. Phys. 113 pp 505– (1987) · Zbl 0633.53089 · doi:10.1007/BF01221257
[13] G.-M. Greuel G. Pfister, H. Schönemann
[14] J. Gray Y.H. He A. Ilderton A. Lukas
[15] Green, Phys. Rev. Lett. 61 pp 1163– (1988) · doi:10.1103/PhysRevLett.61.1163
[16] Candelas, Nucl. Phys. B 330 pp 49– (1990) · doi:10.1016/0550-3213(90)90302-T
[17] Candelas, Nucl. Phys. B 342 pp 246– (1990) · doi:10.1016/0550-3213(90)90577-Z
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