A note on the push-forward formulas for even orthogonal Grassmannians

TL;DR

This paper revisits and corrects residue formulas for the push-forward in the cohomology of even orthogonal Grassmannians, addressing issues related to the space's two components and rectifying previous errors.

Contribution

It provides corrected residue formulas for the cohomology push-forward in even orthogonal Grassmannians, clarifying component-specific formulas and fixing errors in prior literature.

Findings

Corrected residue formulas for each component of the even orthogonal Grassmannian

Clarified the push-forward computation in cohomology for these spaces

Resolved inaccuracies present in earlier works

Abstract

We revisit residue formulas for the push-forward in the cohomology of the even orthogonal Grassmannian. This space has two components, and the formula for a single component demands separate attention. We correct errors spread throughout the literature.