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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Classification up to equivalence of the holomorphic mappings of riemann surfaces of low genus
TL;DR: In this article, a complete classification up to equivalence of the holomorphic mappings of a Riemann surface of genus 3 onto a surface from genus 2 has been given.
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Genus Expanded Cut-and-Join operators and generalized Hurwtiz numbers
TL;DR: In this paper, the authors define genus expanded cut-and-join operators to distinguish the contributions to the generalized Hurwitz number of the source Riemann surface with different genus, by observing carefully the symplectic surgery and the gluing formulas of the relative GW invariants.
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Factorizations of cycles and multi-noded rooted trees
Rosena R. X. Du,Fu Liu +1 more
TL;DR: In this article, it was shown that the number of ways to factor a cycle into a product of cycles of prescribed lengths is O(d^{r-2}.$ The main result of this paper is that there is a bijection from factorizations of a cycle to multi-noded rooted trees via factorization graphs.
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Decomposability problem on branched coverings
TL;DR: In this article, it was shown that any branch data are realized by an indecomposable primitive branched covering on a connected close surface N with Euler's characteristic less than or equal to 0.
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On the center of the Hurwitz graph
TL;DR: In this article, the authors explore the structure of the Hurwitz graph and its connection to the geometric tree graph G_n, and the extended Hurwitz Graph is defined and its properties such as the radius, characterization of some central elements and bounds on the diameter are obtained.
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.