论文标题
在曲线上的Lie代数连接的模量空间上的线束
Line bundles on the moduli space of Lie algebroid connections over a curve
论文作者
论文摘要
我们探索了全体形态空间的代数几何属性lie elgebroid的空间（$ \ Mathcal {l} $）连接在紧凑型Riemann Surface $ x $属$ g \，\ geq \ geq \ geq \ geq \，3 $的紧凑型Riemann Surface $ x $上。构建了$ \ Mathcal {l} $ - 连接的模量空间的平滑压实，以使基础向量束稳定；压缩内部模量空间的补充是分隔线。给出了边界除数的数值有效性的标准。我们计算模量空间的PICARD组，并分析与足够的线束相关的Lie代数Atiyah捆绑包。这使我们能够得出结论，某些谎言代数连接空间的常规功能是常数。此外，在某种情况下，可以证明$ \ Mathcal {l} $的模量空间 - 连接不接受非稳定代数函数。探索了模量空间的合理连接性。
We explore algebro-geometric properties of the moduli space of holomorphic Lie algebroid ($ \mathcal{L} $) connections on a compact Riemann surface $X$ of genus $g \,\geq\, 3$. A smooth compactification of the moduli space of $\mathcal{L}$-connections, such that underlying vector bundle is stable, is constructed; the complement of the moduli space inside the compactification is a divisor. A criterion for the numerical effectiveness of the boundary divisor is given. We compute the Picard group of the moduli space, and analyze Lie algebroid Atiyah bundles associated with an ample line bundle. This enables us to conclude that regular functions on the space of certain Lie algebroid connections are constants. Moreover, under some condition, it is shown that the moduli space of $\mathcal{L}$-connections does not admit non-constant algebraic functions. Rationally connectedness of the moduli spaces is explored.
