Shifted Poisson structures and moduli spaces of complexes
Shifted Poisson structures and moduli spaces of complexes
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DOI：
10.1016/j.aim.2018.09.018
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发表时间：
2017-06
影响因子：
1.7
通讯作者：
Z. Hua;A. Polishchuk
中科院分区：
文献类型：
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作者：
Z. Hua;A. Polishchuk
本文利用导出的代数几何方法研究光滑射影簇X上向量丛复形（具有链同构）的模栈。我们证明了如果X是一个维数为d的Calabi-Yau簇，那么这个模栈有一个（1− d）-移位的泊松结构。在d= 1的情况下，我们通过0-移位辛子栈构造了模栈的自然叶理。我们证明了我们的构造恢复了与复椭圆曲线相关的各种已知的Poisson结构，包括Nevins和斯塔福德研究的椭圆量子投影平面上点的Hilbert方案上的Poisson结构，以及我们之一考虑的椭圆曲线上稳定三元组的模空间上的Poisson结构.我们还涉及后者泊松结构的半经典极限的椭圆Sklyanin代数研究费金和Odesskii。
In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi–Yau variety of dimension d then this moduli stack has a (1− d)-shifted Poisson structure. In the case d= 1, we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii.