Tensored Segre classes

Abstract

We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably simple formulas in standard intersection-theoretic situations such as excess or residual intersections. We prove a formula for the behavior of this class under linear joins, and use this formula to prove that a `Segre zeta function' associated with ideals generated by forms of the same degree is a rational function.

References in corpus (1)

• How many hypersurfaces does it take to cut out a Segre class?

Cited by in corpus (3)

• The Euclidean distance degree of smooth complex projective varieties
• Segre classes and invariants of singular varieties
• The Segre zeta function of an ideal