Ueber Riemann'sche Flächen mit gegebenen Verzweigungspunkten
TLDR
The Riemannsche Theorie der algebraischen Funktionen as discussed by the authors is a Theorie von der graphisch uber der komplexen Zahlenebene.Abstract:
Die grundlegende Bedeutung des vorliegenden Themas fur die Riemann’sche Theorie der algebraischen Funktionen brauche ich wohl kaum hervorzuheben. Geht doch diese Theorie von der graphisch uber der komplexen Zahlenebene konstruierten Riemann’schen Flache aus, um erst sodann die Funktionen, welche durch diese Flache bestimmt sind, zu untersuchen.read more
Citations
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The Number of Ramified Coverings of the Sphere by the Torus and Surfaces of Higher Genera
TL;DR: In this paper, an explicit expression for the number of ramified coverings of the sphere by the torus with given ramification type for a small number of points, and conjecture this to be true for an arbitrary number of Ramification points.
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Integrability of Hurwitz partition functions
Alexander Alexandrov,A. D. Mironov,An. Morozov,Sergey Natanzon,Sergey Natanzon,Sergey Natanzon +5 more
TL;DR: In this article, the authors considered the problem of partition functions of integrable hierarchies, where the partition functions are considered to be dependent on infinite sets of parameters called time variables, and they proposed a partition function Z =?Rd2? kR?R(t(1))??R( t(k))exp?(?n?nCR(n))
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Generation of matrix models by Ŵ-operators
TL;DR: In this article, it was shown that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of operators, and a number of illustrations are given, including the Gaussian Hermitian matrix model, Hermitians model in external field and the Hurwitz-Kontsevitch model, for which they suggest an elegant matrix-model representation.
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Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields
TL;DR: In this article, a homological stabilization theorem for Hurwitz spaces has been proved for moduli spaces of branched covers of the complex projective line, where the moduli space is moduli set of a set of moduli of the modulus space.
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The Topology of Real Projective Algebraic Varieties
TL;DR: A survey of the results on Hilbert's 16th problem from 1876 to the present can be found in this article, where the authors present a survey of Hilbert's methods for constructing M-curves on a quadric.
References
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Ueber die Auflösung gewisser Gleichungen vom siebenten und achten Grade
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Ueber diejenigen algebraischen Gebilde, welche eindeutige Transformationen in sich zulassen
TL;DR: In den nachfolgenden Zeilen beschaftige ich mich namentlich mit der Aufgabe: alle irreduzibeln algebraischen Gleichungen as discussed by the authors.