A REMARK ON VANISHING CYCLES WITH TWO STRATA

Dung Trang Lê (1) , David Massey (2)

1 I2M - Institut de Mathématiques de Marseille
2 Northeastern University [Boston]

Suppose that the critical locus Σ 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 Σ − {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. K

Mots clés: Stratification de Whitney; Vanishing cycles; Perverse sheaf

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]; Variables complexes [math.CV]

Dung Trang Lê, David Massey. A REMARK ON VANISHING CYCLES WITH TWO STRATA. Comptes Rendus. Mathématique, 2012, 350, pp.217 - 220. ⟨hal-01271388⟩