Seminars: N. Ya. Amburg, E. M. Kreines, Belyi pair of the cell decomposition of oriented covering of the Deligne-Mumford compactification for $M^R

SEMINARS


Graphs on surfaces and curves over number fields October 7, 2020, Moscow, online

Belyi pair of the cell decomposition of oriented covering of the Deligne-Mumford compactification for $M^R_{0,5}$ N. Ya. Amburg^ab, E. M. Kreines^c ^a National Research University "Higher School of Economics", Moscow ^b State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow ^c Lomonosov Moscow State University
Abstract: We consider the Deligne-Mamford compactification of the moduli space of genus 0 real algebraic curves with 5 marked and numbered points and its orienting covering. The second one is a surface. So, standard cell decomposition of the original moduli space provides a dessin d'enfant on this surface. We compute the Belyi pair for this dessin. In particular, it appears that the corresponding curve is a celebrated Bring curve.