Remarks on the $L^{2}$-cohomology of singular algebraic surfaces
Remarks on the $L^{2}$-cohomology of singular algebraic surfaces
复制标题
关于奇异代数曲面的$L^{2}$-上同调的备注
DOI：
10.2969/jmsj/04110097
复制
发表时间：
1989
影响因子：
0.7
通讯作者：
M. Nagase
中科院分区：
文献类型：
--
作者：
M. Nagase
$X- s $，我们得到一个不完全黎曼流形$(\mathfrak{X}, g)$。然后Hsiang-Pati在[9]中断言了$L^{2}$-上同调$H_{(2)}^{i}(\mathfrak{X})$与中交同调$IH_{i}^{\overline{m}}(X)$的对偶是自然同构的，这是Cheeger， Goresky和MacPherson [5， \S 4，猜想$C$]的一种特殊情况，它对任何代数变体都成立。然而，他们的证据有一定的差距。在本文中，我们将填补这一空白。因此，我们的主要结果是重申。
$X-S$ , we obtain an incomplete Riemannian manifold $(\mathfrak{X}, g)$ . Then Hsiang-Pati asserted in [9] that the $L^{2}$-cohomology $H_{(2)}^{i}(\mathfrak{X})$ is naturally isomorphic to the dual of the middle intersection homology $IH_{i}^{\overline{m}}(X)$ , which is a special case of the conjecture due to Cheeger, Goresky and MacPherson [5, \S 4, Conjecture $C$] that it holds for any algebraic variety. However their proof has a certain gap. In this paper we will fill it. Our main result is therefore the reassertion.