L-space surgeries on 2-component L-space links

In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits very negative (i.e. $d_1,d_2\ll 0$) L-space surgeries, it is the Hopf link. We also give a way to characterize the torus link $T(2,2l)$ by observing an L-space surgery $S_{d_1,d_2}^3(\mathcal{L})$ with $d_1{d}_2<0$ on a 2-component L-space link with unknotted components. For some 2-component L-space links, we give explicit descriptions of the L-space surgery sets.