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Extremal Polynomials and Riemann Surfaces pp 53–72Cite as

Cell Decomposition of the Moduli Space

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Part of the book series: Springer Monographs in Mathematics ((SMM))

Abstract

For an efficient use of the Chebyshev representation for extremal polynomials we must investigate how the periods of the abelian differential η M behave as functions of a point M in the moduli space. In this chapter we develop a combinatorial geometric approach to the investigation of the period map. To curves M in the moduli space we shall assign in a one-to-one fashion trees Γ of a special form with edges labelled by positive numbers.

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Notes

  1. 1.

    This should not be confused with Γ 0, the intersection of Γ with the real axis.

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  1. Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia

    Andrei Bogatyrev

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Bogatyrev, A. (2012). Cell Decomposition of the Moduli Space. In: Extremal Polynomials and Riemann Surfaces. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25634-9_4

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