Polynomial Roots and Calabi-Yau Geometries

Figure 9

(a) The Hodge numbers, with ℎ^1,1−ℎ^3,1 as the abscissa and ℎ^1,1+ℎ^3,1, the ordinate, of the fourfolds which have vanishing Euler number, and hence rank exceeding unity. (b) The same, but with ℎ^1,1−ℎ^2,1, as the abscissa and ℎ^1,1+ℎ^2,1 as the ordinate. (c) The position of the roots, on the complex plane, of the Poincaré polynomial of these 61 spaces out of the some 3 million.

(a)

(b)

(c)