Intersection Homology & Perverse Sheaves by Laurenţiu G. Maxim

Author:Laurenţiu G. Maxim
Language: eng
Format: epub
ISBN: 9783030276447
Publisher: Springer International Publishing

Let be a pure n-dimensional closed algebraic subvariety with a Whitney stratification . Let be a generic hyperplane (i.e., transversal to all strata of ). Then the natural homomorphism

is an isomorphism for 0 ≤ i ≤ n − 2 and a monomorphism for i = n − 1.

Proof

Let D = X ∩ H and denote by i : D↪X the inclusion map. By Theorem 9.1.1,

is an isomorphism for k < −1 and a monomorphism for k = −1. Furthermore, by the transversality assumption, the inclusion i is locally normally nonsingular, hence

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