Calabi-Yau Three-folds: Poincare Polynomials and Fractals

Details Calabi-Yau Three-folds: Poincare Polynomials and Fractals Calabi-Yau Three-folds: Poincare Polynomials and Fractals

2011-10-07

arxiv.org/abs/1110.1612v1

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 6 figures, invited contribution to the Max Kreuzer Memorial Volume, based on MPhys project of the first author under

Scientific paper

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.

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