We study an Appell hypergeometric system $E_2$ of rank four which is reducible, and show that its Schwarz map admits geometric interpretations: the map can be considered as the universal Abel–Jacobi map of a 1-parameter family of curves of genus 2.
Keiji MATSUMOTO. Takeshi SASAKI. Tomohide TERASOMA. Masaaki YOSHIDA. "An example of Schwarz map of reducible Appell's hypergeometric equation $E_2$ in two variables." J. Math. Soc. Japan 69 (2) 563 - 595, April, 2017. https://doi.org/10.2969/jmsj/06920563