Comparison of the constant sheaf and intersection cohomology on a hypersurface

David B. Massey

Published 2018-01-07Version 1

In the Abelian category of perverse sheaves on a complex analytic space, there is a natural surjection from the shifted constant sheaf on a hypersurface to the intersection cohomology complex. We call the kernel of this morphism the {\bf comparison complex}. In this paper, we show that the comparison complex is isomorphic to the kernel of the identity minus the monodromy on the sheaf of vanishing cycles along the defining function of the hypersurface.