Exact counting of spherical metrics with one conical singularity on rectangular tori

Zhijie Chen, Shihong Zhang

We prove that for every integer $n\ge 2$ and $8\pi (n-1)<\rho <8\pi n$, the singular Liouville equation $Δu+\e^u=ρδ_0$ on a rectangular torus $E_{\mathrm{i}b}=\mathbb{C}/(\mathbb Z+\mathrm{…