The Intersection of holonomy varieties of $CP^1$-structures (2502.11322v2)

Abstract: Let $S$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $S$. We construct infinite pairs of $CP^1$-structures on $X$ and on $Y$ sharing holonomy $\pi_1(S) \to PSL_2 C$.