Vanishing Vanishing Cycles

2006/10/09 by David B. Massey, Massey, David B.
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.AG #msc:32B10 #msc:32B15 #msc:32C18 #msc:32C35

paper · pdf · doi:10.48550/arxiv.math/0610296

11 pages

arxiv created 2010/10/24 · arxiv updated 2010/10/26

Abstract

If \Adot is a bounded, constructible complex of sheaves on a complex analytic space X, and f:X→\C and g:X→\C are complex analytic functions, then the iterated vanishing cycles ϕ_g[-1](ϕ_f[-1]\Adot) are important for a number of reasons. We give a formula for the stalk cohomology H^*(ϕ_g[-1]ϕ_f[-1]\Adot)_x in terms of relative polar curves, algebra, and the normal Morse data and micro-support of \Adot.

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