An inequality for Betti numbers of hyper-Kähler manifolds of dimension 6
An inequality for Betti numbers of hyper-Kähler manifolds of dimension 6
复制标题
6 维超凯勒流形的 Betti 数不等式
DOI：
10.1134/s0001434616010363
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发表时间：
2016
影响因子：
0.6
通讯作者：
N. Kurnosov
中科院分区：
文献类型：
--
作者：
Никон Курносов;N. Kurnosov
一个紧凑的超凯勒流形 M，其中 π1(M) = 0 且 H2,0(M) = C 被认为是简单的（不可约）。根据博戈莫洛夫著名的定理，任何紧致超凯勒流形都承认环面和几个不可约超凯勒流形的乘积的有限覆盖[1]。在复数维度 4 及更高维度中，已知两个系列的超凯勒流形：K3 上 n 点的希尔伯特方案和广义 Kummer 流形 [2]；此外，还有两个由 O’Grady 造成的零星例子（参见[3]、[4]）。已经证明，数值参数不同于上述例子的向量丛的模空间不允许辛分解[5]。
A compact hyper-Kähler manifold M for which π1(M) = 0 and H2,0(M) = C is said to be simple (irreducible). According to Bogomolov’s celebrated theorem, any compact hyper-Kähler manifold admits a finite covering by a product of the torus and several irreducible hyper-Kähler manifolds [1]. In complex dimensions 4 and higher, two series of hyper-Kähler manifolds are known, the Hilbert schemes of n points over K3 and the generalized Kummer manifolds [2]; in addition, there are two sporadic examples due to O’Grady (see [3], [4]). It has been proved that the moduli spaces of vector bundles with numerical parameters different from those in the examples mentioned above admit no symplectic resolution [5].