Polynomial Roots and Calabi-Yau Geometries

TL;DR

This paper explores the roots of specific integer polynomials related to Calabi-Yau spaces, revealing unique geometric patterns and structures such as fractals and holes in the root space.

Contribution

It introduces a detailed analysis of roots of Poincare and Newton polynomials associated with Calabi-Yau geometries, highlighting their distinctive geometric features.

Findings

Identification of fractal structures in root distributions

Discovery of holes and other geometric patterns in root spaces

Insights into the relationship between polynomial roots and Calabi-Yau geometry

Abstract

The examination of roots of constrained polynomials dates back at least to Waring and to Littlewood. However, such delicate structures as fractals and holes have only recently been found. We study the space of roots to certain integer polynomials arising naturally in the context of Calabi-Yau spaces, notably Poincare and Newton polynomials, and observe various salient features and geometrical patterns.