Microlocal sheaves and quiver varieties
Microlocal sheaves and quiver varieties
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微局部滑轮和箭袋品种
DOI：
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发表时间：
2015
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通讯作者：
M. Kapranov
中科院分区：
文献类型：
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作者：
R. Bezrukavnikov;M. Kapranov
我们将中岛箭袋变体（或者更确切地说，它们的乘法版本）与反常滑轮的模空间联系起来。更准确地说，我们考虑反常滑轮概念的推广：节点曲线 X 上的微局部滑轮。它们被定义为在每个节点附近具有傅立叶变换条件的 X 归一化上的反常滑轮，并形成阿贝尔类别 M(X)。一种具有类似的微局部复合体三角类别 DM(X)。对于紧 X，我们证明 DM(X) 是维度 2 的 Calabi-Yau。在 X 的所有分量都是有理数的情况下，M(X) 等价于与 X 的交图相关的乘法预射影代数的表示范畴。正确意义上的箭袋簇是作为微局域滑轮的模空间获得的，在奇点处以消失循环为框架。当 X 的组成部分具有更高的属时，会导致对预投影代数和箭袋簇的有趣概括。我们从伪哈密尔顿约简和群值矩图的角度对它们进行分析。
We relate Nakajima Quiver Varieties (or, rather, their multiplicative version) with moduli spaces of perverse sheaves. More precisely, we consider a generalization of the concept of perverse sheaves: microlocal sheaves on a nodal curve X. They are defined as perverse sheaves on normalization of X with a Fourier transform condition near each node and form an abelian category M(X). One has a similar triangulated category DM(X) of microlocal complexes. For a compact X we show that DM(X) is Calabi-Yau of dimension 2. In the case when all components of X are rational, M(X) is equivalent to the category of representations of the multiplicative pre-projective algebra associated to the intersection graph of X. Quiver varieties in the proper sense are obtained as moduli spaces of microlocal sheaves with a framing of vanishing cycles at singular points. The case when components of X have higher genus, leads to interesting generalizations of preprojective algebras and quiver varieties. We analyze them from the point of view of pseudo-Hamiltonian reduction and group-valued moment maps.