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The Hodge numbers of generic elliptically fibered Calabi-Yau threefolds over toric base surfaces fill out the "shield" structure previously identified by Kreuzer and Skarke.
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A. Grassi, D. R. Morrison, “Group representations and the Euler characteristic of elliptically fibered Calabi-Yau threefolds”, J. Algebraic Geom. 12 (2003), 321-356 arXiv:math/0005196
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