INTERSECTION COHOMOLOGY, MONODROMY AND THE MILNOR FIBER

被引:5
作者
Massey, David B. [1 ]
机构
[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA
关键词
Intersection cohomology; monodromy; Milnor fiber; vanishing cycles; THEOREM;
D O I
10.1142/S0129167X0900539X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页码:491 / 507
页数:17
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