We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Chern classes of blow-ups.
- Authors
Aluffi, Paolo
- Abstract
We extend the classical formula of Porteous for blowing-up Chern classes to the case of blow-ups of possibly singular varieties along regularly embedded centers. The proof of this generalization is perhaps conceptually simpler than the standard argument for the nonsingular case, involving Riemann-Roch without denominators. The new approach relies on the explicit computation of an ideal, and a mild generalization of a well-known formula for the normal bundle of a proper transform ([8, B∙6∙10]). We also discuss alternative, very short proofs of the standard formula in some cases: an approach relying on the theory of Chern-Schwartz-MacPherson classes (working in characteristic 0), and an argument reducing the formula to a straightforward computation of Chern classes for sheaves of differential 1-forms with logarithmic poles (when the center of the blow-up is a complete intersection).
- Subjects
CHERN classes; BLOWING up (Algebraic geometry); RIEMANN-Roch theorems; TANGENT bundles; DIVISOR theory
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2010, Vol 148, Issue 2, p227
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004109990247