Flag bundles, Segre polynomials and push-forwards

TL;DR

This paper derives new Gysin formulas for partial flag bundles and Schubert varieties in Grassmann bundles, providing a unified approach that yields a comprehensive set of universal formulas for classical groups.

Contribution

It introduces a uniform method to compute Gysin formulas for flag bundles and Schubert varieties, expanding the toolkit for algebraic geometry calculations.

Findings

Derived Gysin formulas for partial flag bundles of classical groups

Established Gysin formulas for Schubert varieties in Grassmann bundles

Provided a unified construction approach for these formulas

Abstract

In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way by using the step-by-step construction of flag bundles and the Gysin formula for a projective bundle. In this way we obtain a comprehensive list of new universal formulas.