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- W3158705891 abstract "We propose definitions of complex manifolds $mathcal{P}_M(X,m,n)$ that could potentially be used to construct the symplectic Khovanov homology of $n$-stranded links in lens spaces. The manifolds $mathcal{P}_M(X,m,n)$ are defined as moduli spaces of Hecke modifications of rank 2 parabolic bundles over an elliptic curve $X$. To characterize these spaces, we describe all possible Hecke modifications of all possible rank 2 vector bundles over $X$, and we use these results to define a canonical open embedding of $mathcal{P}_M(X,m,n)$ into $M^s(X,m+n)$, the moduli space of stable rank 2 parabolic bundles over $X$ with trivial determinant bundle and $m+n$ marked points. We explicitly compute $mathcal{P}_M(X,1,n)$ for $n=0,1,2$. For comparison, we present analogous results for the case of rational curves, for which a corresponding complex manifold $mathcal{P}_M(mathbb{CP}^1,3,n)$ is isomorphic for $n$ even to a space $mathcal{Y}(S^2,n)$ defined by Seidel and Smith that can be used to compute the symplectic Khovanov homology of $n$-stranded links in $S^3$." @default.
- W3158705891 created "2021-05-10" @default.
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- W3158705891 date "2021-04-25" @default.
- W3158705891 modified "2023-10-10" @default.
- W3158705891 title "Moduli spaces of Hecke modifications for rational and elliptic curves" @default.
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- W3158705891 doi "https://doi.org/10.2140/agt.2021.21.543" @default.
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