Fiber integration on the Demailly tower

TL;DR

This paper develops a new fiber integration formula on the Demailly tower that simplifies computations by avoiding step-by-step elimination, using a recursive approach and an iterated residue formula.

Contribution

It introduces a natural twist of the Demailly tower and derives a recursive formula for the total Segre class, enabling more effective calculations.

Findings

Derived a recursive formula for the total Segre class.

Established an iterated residue formula for Segre classes.

Provided a computationally effective fiber integration method.

Abstract

The goal of this work is to provide a fiber integration formula on the Demailly tower, that avoids step-by-step elimination of horizontal cohomology classes, and that yields computational effectivity. A natural twist of the Demailly tower is introduced and a recursive formula for the total Segre class at k-th level is obtained. Then, by interpreting single Segre classes as coefficients, an iterated residue formula is derived.