The Enriquez connection for higher genus polylogarithms

Puntos clave

• The aim is to investigate the Enriquez connection for higher genus polylogarithms and its behavior during Riemann surface degenerations.
• Studied variations of the Enriquez connection in relation to Riemann surfaces with marked points.
• Analyzed the connection's transition to the author's previously established connection for degenerating families.
• Described higher genus polylogarithms as power series based on deformation parameters.
• Established a connection between higher genus polylogarithms and multiple zeta values through explicit descriptions.
• Demonstrated a clear transition of the connections under degeneration of Riemann surfaces.

Resumen