On the Moduli of SL ( 2 )-bundles with Connections on P 1 { x 1 ,
On the Moduli of SL ( 2 )-bundles with Connections on P 1 { x 1 ,
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关于具有 P 1 { x 1 上的连接的 SL ( 2 )-丛的模，
DOI：
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发表时间：
1997
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通讯作者：
S. Lysenko
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作者：
D. Arinkin;S. Lysenko
代数曲线上具有联络的丛的模空间已经从不同的角度得到了研究（见[6]，[10]）。我们对这个问题的兴趣是由于它与Painlevé方程的关系，以及几何Langlands纲领[4]中具有联络的丛的重要作用（更多细节见引言末尾的评论）。本文考虑P1上的SL（2）-丛的连通性。假设这些联络在固定的n个点上有1阶极点，并且留数的特征值±λi是固定的。我们称这些丛为（λ1，. . .，λn）-丛。我们的目标是找到模空间（λ1，λ 2）上的所有可逆层。. .，λn）-丛，并计算了n = 4时这些层的上同调.在这项工作中，基场是C，也就是说，“空间”意味着“C-空间”，P1意味着PC，等等。让我们用公式表示这项工作的主要结果。修复x1，. . .，xn ∈ P1（C），n ≥ 4，xi 6= xj，其中i 6= j，且λ1，. . .，λn ∈ C.
The moduli spaces of bundles with connections on algebraic curves have been studied from various points of view (see [6], [10]). Our interest in this subject was motivated by its relation with the Painlevé equations, and also by the important role of bundles with connections in the geometric Langlands program [4] (for more details see the remarks at the end of the introduction). In this work, we consider SL(2)-bundles on P1 with connections. These connections are supposed to have poles of order 1 at fixed n points, and the eigenvalues ±λi of the residues are fixed. We call these bundles (λ1, . . . , λn)-bundles. Our aim is to find all invertible sheaves on the moduli space of (λ1, . . . , λn)-bundles and to compute the cohomology of these sheaves for n = 4. In this work, the ground field is C, that is, ‘space’ means ‘C-space’, P1 means PC, and so on. Let us formulate the main results of this work. Fix x1, . . . , xn ∈ P1(C), n ≥ 4, xi 6= xj for i 6= j, and λ1, . . . , λn ∈ C.