Calabi-Yau Three-folds: Poincare Polynomials and Fractals

Abstract

We study the Poincare polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the well-known investigation into the distribution of the Euler characteristic and Hodge numbers. We find interesting fractal behaviour in the roots of these polynomials in relation to the existence of isometries, distribution versus typicality, and mirror symmetry.

arXiv comment14 pages, 6 figures, invited contribution to the Max Kreuzer Memorial Volume, based on MPhys project of the first author under the supervision of the second, at the University of Oxford

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