INTERSECTION COHOMOLOGY, MONODROMY AND THE MILNOR FIBER
INTERSECTION COHOMOLOGY, MONODROMY AND THE MILNOR FIBER
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交交上同调、单调和 MILNOR 纤维
DOI：
10.1142/s0129167x0900539x
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发表时间：
2004
影响因子：
0.6
通讯作者：
D. Massey
中科院分区：
文献类型：
--
作者：
D. Massey
我们说一个复解析空间X是一个交上同调流形当且仅当X上的移位常数层同构于交上同调;对于域系数，这很快就等价于X是一个同调流形。给定一个交上同调流形上的解析函数f，我们描述了V（f）是一个交上同调流形与f的消失圈Milnor单值性之间的一个简单关系.然后，我们描述了如何让我们很容易地产生任意奇异集的相交上同调流形的Ratiani-Thom同构。最后，作为一个简单的应用，我们得到了具有特殊类型的一维临界轨迹的超曲面的Milnor纤维的上同调的限制。
We say that a complex analytic space, X, is an intersection cohomology manifold if and only if the shifted constant sheaf on X is isomorphic to intersection cohomology; with field coefficients, this is quickly seen to be equivalent to X being a homology manifold. Given an analytic function f on an intersection cohomology manifold, we describe a simple relation between V(f) being an intersection cohomology manifold and the vanishing cycle Milnor monodromy of f. We then describe how the Sebastiani–Thom isomorphism allows us to easily produce intersection cohomology manifolds with arbitrary singular sets. Finally, as an easy application, we obtain restrictions on the cohomology of the Milnor fiber of a hypersurface with a special type of one-dimensional critical locus.