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- W2994467322 abstract "Let $S$ be a finite subset of a compact connected Riemann surface $X$ of genus $g geq 2$. Let $cat{M}_{lc}(n,d)$ denote the moduli space of pairs $(E,D)$, where $E$ is a holomorphic vector bundle over $X$ and $D$ is a logarithmic connection on $E$ singular over $S$, with fixed residues in the centre of $mathfrak{gl}(n,C)$, where $n$ and $d$ are mutually corpime. Let $L$ denote a fixed line bundle with a logarithmic connection $D_L$ singular over $S$. Let $cat{M}'_{lc}(n,d)$ and $cat{M}_{lc}(n,L)$ be the moduli spaces parametrising all pairs $(E,D)$ such that underlying vector bundle $E$ is stable and $(bigwedge^nE, tilde{D}) cong (L,D_L)$ respectively. Let $cat{M}'_{lc}(n,L) subset cat{M}_{lc}(n,L)$ be the Zariski open dense subset such that the underlying vector bundle is stable. We show that there is a natural compactification of $cat{M}'_{lc}(n,d)$ and $cat{M}'_{lc}(n,L)$ and compute their Picard groups. We also show that $cat{M}'_{lc}(n,L)$ and hence $cat{M}_{lc}(n,L)$ do not have any non-constant algebraic functions but they admit non-constant holomorhic functions. We also study the Picard group and algebraic functions on the moduli space of logarithmic connections singular over $S$, with arbitrary residues." @default.
- W2994467322 created "2019-12-13" @default.
- W2994467322 creator A5005968723 @default.
- W2994467322 date "2019-12-03" @default.
- W2994467322 modified "2023-09-27" @default.
- W2994467322 title "Moduli space of logarithmic connections singular over a finite subset of a compact Riemann surface" @default.
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