zbMATH — the first resource for mathematics

A remark on generalized complete intersections. (English) Zbl 1375.81198
Summary: We observe that an interesting method to produce non-complete intersection subvarieties, the generalized complete intersections from L. Anderson and coworkers, can be understood and made explicit by using standard Cech cohomology machinery. We include a worked example of a generalized complete intersection Calabi-Yau threefold.
Reviewer: Reviewer (Berlin)

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14J30 \(3\)-folds
55N05 Čech types
Full Text: DOI
[1] Anderson, L. B.; Apruzzi, F.; Gao, X.; Gray, J.; Lee, S-J., A new construction of Calabi-Yau manifolds: generalized cicys, Nucl. Phys. B, 906, 441-496, (2016) · Zbl 1334.14023
[2] Anderson, L. B.; Apruzzi, F.; Gao, X.; Gray, J.; Lee, S-J., Instanton superpotentials, Calabi-Yau geometry, and fibrations, Phys. Rev. D, 93, 8, (2016)
[3] Altman, R.; Gray, J.; He, Y-H.; Jejjalaf, V.; Nelson, B. D., A Calabi-Yau database: threefolds constructed from the kreuzer-skarke List, J. High Energy Phys., 2, (2015) · Zbl 1388.53071
[4] Berglund, P.; Hübsch, T., On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations · Zbl 1420.14090
[5] Candelas, P.; Constantin, A.; Mishra, C., Calabi-Yau threefolds with small Hodge numbers
[6] Constatin, A.; Gray, J.; Lukas, A., Hodge numbers for all CICY quotients, J. High Energy Phys., 01, 001, (2017)
[7] Coughlan, S.; Golebiowski, L.; Kapustka, G.; Kapustka, M., Arithmetically Gorenstein Calabi-Yau threefolds in \(P^7\), Electron. Res. Announc. Math. Sci., 23, 52-68, (2016) · Zbl 1404.14049
[8] van Geemen, B.; Sarti, A., Nikulin involutions on K3 surfaces, Math. Z., 255, 731-753, (2007) · Zbl 1141.14022
[9] Ito, A.; Miura, M.; Okawa, S.; Ueda, K., Calabi-Yau complete intersections in \(G_2\)-Grassmannians
[10] Kapustka, G.; Kapustka, M., Calabi-Yau threefolds in \(P^6\), Ann. Mat. Pura Appl., 195, 529-556, (2016) · Zbl 1350.14030
[11] Kreuzer, M.; Skarke, H., Complete classification of reflexive polyhedra in four-dimensions, Adv. Theor. Math. Phys., 4, 1209, (2002) · Zbl 1017.52007
[12] Bosma, W.; Cannon, J.; Playoust, C., The magma algebra system. I. the user language, J. Symb. Comput., 24, 235-265, (1997) · Zbl 0898.68039
[13] Voisin, C., Hodge theory and complex algebraic geometry I, (2002), Cambridge University Press · Zbl 1005.14002
[14] Wilson, P. M.H., Boundedness questions for Calabi-Yau threefolds
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.