On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties
On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties
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DOI：
10.1090/tran/8592
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发表时间：
2021-08
影响因子：
1.3
通讯作者：
Camilla Felisetti;Junliang Shen;Qizheng Yin
中科院分区：
文献类型：
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作者：
Camilla Felisetti;Junliang Shen;Qizheng Yin
.我们证明了几个结果有关的交叉上同调和反常过滤与拉格朗日纤维化的不可约辛簇。我们首先证明了反常数只依赖于环境簇的变形等价类。然后我们计算了反常菱形的边界，进一步得到了拉格朗日基的交上同调和纤维的不变上同调类的完整描述。最后，当不可约辛簇有辛分解时，我们确定了交上同调的逆数和霍奇数。这些结果推广了第二和第三作者在非奇异情形下的一些早期工作。
. We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an ir- reducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute the border of the perverse diamond, which further yields a complete description of the intersection cohomology of the Lagrangian base and the in- variant cohomology classes of the fibers. Lastly, we identify the perverse and Hodge numbers of intersection cohomology when the irreducible symplectic variety admits a symplectic resolution. These results generalize some earlier work by the second and third authors in the nonsingular case.