MacPherson, Robert; Vilonen, Kari Perverse sheaves with singularities along the curve \(y^ n=x^ m\). (English) Zbl 0638.32014 Comment. Math. Helv. 63, No. 1, 89-102 (1988). The authors prove that the category of perverse sheaves on the complex two-space \({\mathbb{C}}^ 2\), constructible with respect to the stratification \(\{0\}\subset \{y^ n=x^ m\}\subset {\mathbb{C}}^ 2\), \(n\leq m\), is equivalent to the category of \((n+2)\)-tuples of vector spaces \(A,B_ 1,...,B_ n,C\) together with maps \(A\rightleftarrows^{q_ k}_{p_ k}B_ k\rightleftarrows^{s_ k}_{r_ k}C\) and \(\theta_ k:B_ k\to B_{k+m}\) (all the indices are to be considered as integers modulo n), which satisfy some relations, explicitely given. The proof uses methods of the authors given in C. R. Acad. Sci., Paris, Ser. I. 299, 443-446 (1984; Zbl 0581.14013), and Invent. Math. 84, 403-435 (1986; Zbl 0597.18005). As an application one classifies perverse sheaves with no vanishing cycles at the origin for the case \(y^ 2=x^ 3\); in this case the nontrivial irreducible perverse sheaves are parameterized by one complex number. Reviewer: Vasile Brînzănescu Cited in 3 ReviewsCited in 16 Documents MSC: 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 32B15 Analytic subsets of affine space 14E20 Coverings in algebraic geometry Keywords:fundamental group; perverse sheaves; stratification Citations:Zbl 0581.14013; Zbl 0597.18005 PDFBibTeX XMLCite \textit{R. MacPherson} and \textit{K. Vilonen}, Comment. Math. Helv. 63, No. 1, 89--102 (1988; Zbl 0638.32014) Full Text: DOI EuDML