107 citations
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4 papers · 1 filter
Algebraic Independence of generic Painlevé Transcendents: P_III and P_VI
Joel Nagloo
We prove that if y"=f(y,y',t) is a generic Painlevé equation from the class III and VI, and if y_1,...,y_n are distinct solutions, then y_1,y_1',...,y_n,y_n' are algebraically inde…
On Transformations in the Painlevé Family
Joel Nagloo
In this paper we show that generic Painlevé equations from different families are orthogonal. In particular, this means that there are no general Backlund transformations between P…
Classical curves via one-vertex maps
Anthony Weaver
One-vertex maps (a type of dessin d'enfant) give a uniform characterization of certain well-known algebraic curves, including those of Klein, Wiman, Accola-Maclachlan and Kulkarni.…
Exceptional points in the elliptic-hyperelliptic locus
Ewa Tyszkowska, Anthony Weaver
An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a…