Moduli spaces of Hecke modifications for rational and elliptic curves
| Autor: | Boozer, David |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Algebr. Geom. Topol. 21 (2021) 543-600 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/agt.2021.21.543 |
| Popis: | 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 $S^3$. Comment: 29 pages, 1 figure; extensively revised; new methods are used to describe Hecke modifications in order to obtain more concise proofs |
| Databáze: | arXiv |
| Externí odkaz: |
|