Combinatorial analysis of the period mapping: the topology of 2D fibres

Abstract

Abstract We study the period mapping from the moduli space of real hyperelliptic curves to a Euclidean space. The mapping arises in the analysis of Chebyshev’s construction used in the constrained optimization of the uniform norm of polynomials and rational functions. The decomposition of the moduli space into polyhedra labelled by planar graphs allows us to investigate the global topology of low-dimensional fibres of the period mapping. Bibliography: 23 titles.