Define Segre classes for cone stacks in general

Define Segre classes for arbitrary cone stacks, extending the total Segre class construction used for cone stacks that admit a global presentation as a quotient of a cone by a vector bundle.

Background

The paper defines the total Segre class of a cone stack only when the cone stack has a global presentation of the form [C/T], where C is a cone and T is a vector bundle acting on C. In that setting, the class is defined by c(T) cap s(C), and the authors prove that it is independent of the chosen global presentation.

The authors note that this construction does not provide a general definition for cone stacks lacking such a global presentation. A general theory would broaden the applicability of Fulton-class and Siebert-formula methods beyond the globally presentable case.

References

Segre classes of cone stacks are not, to our knowledge, defined in general, but we can state the following definition and lemma.

— Virtual classes: An introduction with exercises  (2609.18454 - Lu et al., 16 Sep 2026) in Section 9, subsection “Fulton’s class”