Perverse sheaves with singularities along the curve \(y^ n=x^ m\)
type: Item
instance of: scholarly article
title: Perverse sheaves with singularities along the curve \(y^ n=x^ m\)
zbMATH Open document ID: 0638.32014
DOI: 10.1007/BF02566754
author: Robert MacPherson
author: Kari Vilonen
published in: Commentarii Mathematici Helvetici
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/140110
review text: 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.
reviewed by: Vasile Brînzănescu
Mathematics Subject Classification ID: 32S60
Mathematics Subject Classification ID: 32B15
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 4040291
zbMATH Keywords: fundamental group
zbMATH Keywords: perverse sheaves
zbMATH Keywords: stratification
MaRDI profile type: Publication
OpenAlex ID: W2062969156
description: scientific article; zbMATH DE number 4040291