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Calabi-Yau Geometries: Algorithms, Databases, and Physics

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Figure 1: (a) The space of CY3, with the 3 most studied datasets. There are also some indi-most “typical” CY3 has Hodge numbersχvidualized constructions outside the three major databases, symbolically marked as crosses;these have been tabulated [9, 43, 45]
Figure 2: (a) A colour Log-density plot of the Hodge numbers of the KS dataset, withχ = 2(h1,1 − h1,2) (horizontal) versus h1,1 + h1,2 (vertical)
Figure 3: (a) The space of local (affine) CY3 thus far charted. The crosses symbolizeisolated cases and the Venn diagram are the major families studied
Figure 4: The toric diagrams of some partial resolutions (sub-diagrams) of the Abelianorbifold C3/Z23, as well as the quivers for the engineered 4d N = 1 gauge theories

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