Verdier specialization via weak factorization

Paolo Aluffi Mathematics Department, Florida State University

K-Theory and Homology mathscidoc:1701.01019

Arkiv for Matematik, 51, (1), 1-28, 2010.10
Let$X$⊂$V$be a closed embedding, with$V$∖$X$nonsingular. We define a constructible function$ψ$_{$X$,$V$}on$X$, agreeing with Verdier’s specialization of the constant function$1$_{$V$}when$X$is the zero-locus of a function on$V$. Our definition is given in terms of an embedded resolution of$X$; the independence of the choice of resolution is obtained as a consequence of the weak factorization theorem of Abramovich–Karu–Matsuki–Włodarczyk. The main property of$ψ$_{$X$,$V$}is a compatibility with the specialization of the Chern class of the complement$V$∖$X$. With the definition adopted here, this is an easy consequence of standard intersection theory. It recovers Verdier’s result when$X$is the zero-locus of a function on$V$.
No keywords uploaded!
[ Download ] [ 2017-01-08 20:36:34 uploaded by arkivadmin ] [ 299 downloads ] [ 0 comments ] [ Cited by 1 ]
  title={Verdier specialization via weak factorization},
  author={Paolo Aluffi},
  booktitle={Arkiv for Matematik},
Paolo Aluffi. Verdier specialization via weak factorization. 2010. Vol. 51. In Arkiv for Matematik. pp.1-28.
Please log in for comment!
Contact us: | Copyright Reserved