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Combinatorial analysis of the period mapping: the topology of 2D fibres A. B. Bogatyrev Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia 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. Keywords: moduli space, real algebraic curve, Abelian integral, period mapping, foliations of a quadratic differential.
DOI: https://doi.org/10.4213/sm8904   Full text:
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English version: Sbornik: Mathematics, 2019, 210:11, Bibliographic databases:    
UDC: 517.54+519.1+514.76 MSC: Primary 30F30; Secondary 32G15, 05E45 Received: 31.12.2016 and 24.06.2019 Citation: A. B. Bogatyrev, “Combinatorial analysis of the period mapping: the topology of 2D fibres”, Mat. Sb., 210:11 (2019), 
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