Equivariant Hirzebruch class for quadratic cones via degenerations

TL;DR

This paper calculates the equivariant Hirzebruch class of quadratic cones in complex space, analyzing their degeneration to hyperplanes and revealing relationships with Milnor classes and complements.

Contribution

It introduces a method to compute the equivariant Hirzebruch class for quadratic cones using degenerations to hyperplanes, linking it to Milnor classes.

Findings

Hirzebruch class of quadratic cones is computed explicitly.

Degeneration to hyperplanes relates the class to smaller-dimensional complements.

Difference measured by Milnor class captures geometric transitions.

Abstract

We compute the equivariant Hirzebruch class of the quadric cone in C^n degenerating it to an intersection to hyperplanes. The difference of the Hirzebruch classes (measured by the Milnor class) turns out to be the Hirzebruch class of the complement of the quadratic cone of smaller dimension.