Calabi-Yau Three-folds: Poincare Polynomials and Fractals

Ashmore, A. & He, Y. (2011). Calabi-Yau Three-folds: Poincare Polynomials and Fractals. In: Strings, Gauge Fields, and the Geometry Behind: The Legacy of Maximilian Kreuzer. (pp. 173-186). World Scientific Publishing Company. ISBN 978-981-4412-54-4

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We study the Poincar´e polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the wellknown 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.

Item Type: Book Section
Additional Information: Calabi-Yau Three-folds: Poincare Polynomials and Fractals, YANG-HUI HE, Copyright 2011 with permission from World Scientific Publishing Co. Pte. Ltd.
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science

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