A Deterministic Method for Computing Bertini Type Invariants of Parametric Ideals

Abstract

A new framework is proposed for computing general numerical invariants, called Bertini type invariants, associated to a family of polynomial ideals depending on deformation parameters. A deterministic algorithm is introduced for computing parameter dependency of Bertini type invariants. As an application, an algorithm for computing Chern–Schwartz–MacPherson classes of a family of singular projective hypersurfaces is obtained.