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We consider the fractional Hartree equation in the $L^2$-supercritical case,and we find a sharp threshold of the scattering versus blow-up dichotomy forradial data: If $M[u_{0}]^{\frac{s-s_c}{s_c}}E[u_{0}<M[Q]^{\frac{s-s_c}{s_c}}E[Q]$ and$M[u_{0}]^{\frac{s-s_c}{s_c}}\|u_{0}\|^2_{\dot H^s}<M[Q]^{\frac{s-s_c}{s_c}}\|Q\|^2_{\dot H^s}$, then the solution $u(t)$ is globally well-posed andscatters; if $M[u_{0}]^{\frac{s-s_c}{s_c}}E[u_{0}]<M[Q]^{\frac{s-s_c}{s_c}}E[Q]$ and$M[u_{0}]^{\frac{s-s_c}{s_c}}\|u_{0}\|^2_{\dot H^s}>M[Q]^{\frac{s-s_c}{s_c}}\|Q\|^2_{\dot H^s}$, the solution $u(t)$ blows up in finite time. This conditionis sharp in the sense that the solitary wave solution $e^{it}Q(x)$ is globalbut not scattering, which satisfies the equality in the above conditions. Here,$Q$ is the ground-state solution for the fractional Hartree equation.

Sharp Threshold of Blow-up and Scattering for the fractional Hartree equation