论文标题
抛物线连接的模量空间上的线束
Line bundles on the moduli space of parabolic connections over a compact Riemann surface
论文作者
论文摘要
令$ x $为$ g \ geq 3 $和$ s $的紧凑型Riemann Surface $ x $。令$ξ$修复了一个超过$ x $ $ d $的全态线捆绑包。令$ \ MATHCAL {M} _ {PC}（R，D，α）$（分别分别为$ \ Mathcal {M} _ {pc}（r，α，α，ξ）$）表示等级$ r $的寄生虫连接的Moduli空间，$ r $，d $ d $ d $ d $ d $ d $ $ d $ $ d $ $ d $ n $ n $ n $（分别）（分别）抛物线点$ s \ subset x $。 令$ \ MATHCAL {M}'_ {PC}（r，d，α）$（分别分别为$ \ Mathcal {M}'_ {PC}（R，r，α，ξ）$）为Zariski密集的开放式子集$ \ Mathcal {m} $ \ MATHCAL {M} _ {PC}（R，α，ξ）$）参数所有抛物线连接，以使基础抛物线束稳定。我们表明，模量空间$ \ mathcal {m}'_ {pc}（r，d，α）$和$ \ mathcal {m}'_ {pc}（r，α，α，ξ）$ by Smooth Divisors by Smooth Divisors。 我们描述了这些分隔线在无穷大的数字有效性。我们确定Moduli空间的PICARD组$ \ MATHCAL {M} _ {PC}（r，d，d，α）$和$ \ MATHCAL {M} _ {PC}（R，α，ξ）$。令$ \ MATHCAL {C}（L）$表示抛物线捆绑包的Moduli Space $ \ Mathcal {M}（r，d，d，α）$上的充分线束$ l $上的Holomorthic Connections的空间。我们表明，$ \ Mathcal {C}（L）$不接受任何非稳定代数函数。
Let $X$ be a compact Riemann surface of genus $g \geq 3$ and $S$ a finite subset of $X$. Let $ξ$ be fixed a holomorphic line bundle over $X$ of degree $d$. Let $\mathcal{M}_{pc}(r, d, α)$ (respectively, $\mathcal{M}_{pc}(r, α, ξ)$ ) denote the moduli space of parabolic connections of rank $r$, degree $d$ and full flag rational generic weight system $α$, (respectively, with the fixed determinant $ξ$) singular over the parabolic points $S \subset X$. Let $\mathcal{M}'_{pc}(r, d, α)$ (respectively, $\mathcal{M}'_{pc}(r, α, ξ)$) be the Zariski dense open subset of $\mathcal{M}_{pc}(r, d, α)$ (respectively, $\mathcal{M}_{pc}(r, α, ξ)$ )parametrizing all parabolic connections such that the underlying parabolic bundle is stable. We show that there is a natural compactification of the moduli spaces $\mathcal{M}'_{pc}(r, d, α)$, and $\mathcal{M}'_{pc}(r, α, ξ)$ by smooth divisors. We describe the numerically effectiveness of these divisors at infinity. We determine the Picard group of the moduli spaces $\mathcal{M}_{pc}(r, d, α)$, and $\mathcal{M}_{pc}(r, α, ξ)$. Let $\mathcal{C}(L)$ denote the space of holomorphic connections on an ample line bundle $L$ over the moduli space $\mathcal{M}(r, d, α)$ of parabolic bundles. We show that $\mathcal{C}(L)$ does not admit any non-constant algebraic function.
