Moduli spaces of Hecke modifications for rational and elliptic curves

We propose definitions of complex manifolds $\mathcal{P}_M(X,m,n)$ that could potentially be used to construct the symplectic Khovanov homology $n$-stranded links in lens spaces. The are defined as moduli spaces Hecke modifications rank 2 parabolic bundles over an elliptic curve $X$. To characterize these spaces, we describe all possible vector $X$, and use results define a canonical open embedding into $M^s(X,m+n)$, space stable $X$ with trivial determinant bundle $m+n$ marked points. explicitly compute $\mathcal{P}_M(X,1,n)$ for $n=0,1,2$. For comparison, present analogous case rational curves, which corresponding manifold $\mathcal{P}_M(\mathbb{CP}^1,3,n)$ is isomorphic $n$ even $\mathcal{Y}(S^2,n)$ by Seidel Smith can $S^3$.