Diagonals of flag bundles

TL;DR

This paper investigates the geometric properties of diagonals and point subschemes in flag bundles, providing explicit formulas and conditions for complex manifolds related to algebraic groups.

Contribution

It expresses diagonals of various flag bundles as zero schemes of vector bundle sections and explores their properties and formulas.

Findings

Diagonals of flag bundles can be described as zero schemes of vector bundle sections.

Explicit formulas for the classes of diagonals in G/B varieties are derived.

Conditions for point and diagonal properties in complex G/B manifolds are discussed.

Abstract

We express the diagonals of projective, Grassmann and, more generally, flag bundles of type (A) using the zero schemes of some vector bundle sections, and do the same for their single point subschemes. We discuss diagonal and point properties of these flag bundles. We study when the complex manifolds G/B for other groups have the point and diagonal properties. We discuss explicit formulas for the classes of diagonals of the varieties G/B.