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# Deformed dessins d'enfants of almost Belyi maps

Raimundas Vidunas (Institute of Applied Mathematics, Vilnius University, Lithuania)
Thursday, 11 April 2019
15:40
401

Almost Belyi maps are algebraic maps to P^1\{0,1,infiity} with exactly one (simple) branching point. As I explain from sratch, almost Belyi maps form 1-dimensional families. Their degenerations to Belyi maps are defined by image of braid monodromy as a Belyi map from the 1-dimensional base curve. I describe the geometric analogue of dessins d'enfants corresponding to almost Belyi maps. Special almost Belyi maps give isomonodromic Fuchsian differential equations corresponding to algebraic solutions of the Painleve VI equation.