Intersection of holonomy varieties of $CP^1$-structures

Shinpei Baba

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arXiv · 2502.11322

Intersection of holonomy varieties of $CP^1$-structures

Shinpei Baba

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Abstract

Let $\Sigma$ be a closed orientable surface of genus at least two, and let $X, Y$ be distinct marked Riemann surface structures on $\Sigma$, possibly with opposite orientations. In this paper, we show that there are (exactly) countably infinite pairs of ${\rm CP}^1$-structures on $X$ and on $Y$ sharing holonomy $\pi_1(\Sigma) \to {\rm PSL}_2 {\rm C}$.

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Shinpei Baba. 2025-02-17. Intersection of holonomy varieties of $CP^1$-structures. https://arxiv.org/abs/2502.11322

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