On the specialization to the asymptotic cone

Abstract

Let X be a smooth, connected, closed subvariety of a complex vector space V. The asymptotic cone as(X) is naturally equipped with a nearby cycles sheaf P coming from the specialization of X to as(X). We show that if X is transverse to infinity in a suitable sense, then the Fourier transform of P is an intersection homology sheaf.

17 pages, 2 figures, AMSLaTeX. At the moment, there is some overlap between this paper and math.AG/9802042

References in corpus (2)

• Morse groups in symmetric spaces corresponding to the symmetric group
• A generalization of Springer theory using nearby cycles

Cited by in corpus (7)

• Nearby Cycle Sheaves for Symmetric Pairs
• Nearby Cycle Sheaves for Stable Polar Representations
• Character sheaves for symmetric pairs: special linear groups
• Errata and notes on the paper "A generalization of Springer theory using nearby cycles"
• A generalization of Springer theory using nearby cycles
• Character sheaves for classical symmetric pairs
• Invariant systems and character sheaves for graded Lie algebras