A remark on vanishing cycles with two strata

Details A remark on vanishing cycles with two strata A remark on vanishing cycles with two strata

2011-08-19

arxiv.org/abs/1108.3945v1

Mathematics

Algebraic Geometry

A 3-page note

Scientific paper

Suppose that the critical locus $\Sigma$ of a complex analytic function $f$ on affine space is, itself, a space with an isolated singular point at the origin $\0$, and that the Milnor number of $f$ restricted to normal slices of $\Sigma-\{\0\}$ is constant. Then, the general theory of perverse sheaves puts severe restrictions on the cohomology of the Milnor fiber of $f$ at $\0$, and even more surprising restrictions on the cohomology of the Milnor fiber of generic hyperplane slices.

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