Stability of tri-canonical curves of genus two

Abstract

We completely classify tri-canonically embedded curves of genus two that are Chow semistable, and identify the moduli space of them with the compact moduli space of binary sextics. This moduli space is the log canonical model for the pair \(\big(\overline{M}_2,\alpha\Delta_0+\frac{1+\alpha}{2}\Delta_1+\frac{1}{2}\Xi\big)\) for 7/10 \(< \alpha \le\) 9/11 whose log canonical divisor pulls back to \(K_{\overline{M}_2}+\alpha\delta\) on the moduli stack