Moduli of toric principal bundles

TL;DR

This paper constructs a moduli space for toric principal G-bundles using a classification by piecewise linear maps, extending prior work on toric vector bundles.

Contribution

It introduces a new moduli space for toric principal bundles with fixed characteristic class, generalizing previous vector bundle results.

Findings

Constructed a moduli space as a locally closed subvariety of partial flag varieties.

Extended the classification of toric bundles to principal G-bundles.

Generalized the moduli construction from vector bundles to principal bundles.

Abstract

Let $G$ be a reductive algebraic group. A toric principal $G$-bundle is a principal $G$-bundle over a toric variety together with a torus action commuting with the $G$-action. Extending the Klyachko classification of toric vector bundles, Kaveh-Manon classify toric principal bundles by piecewise linear maps to the (extended) Tits building of $G$. In this paper, we use this classification to construct a moduli space of (framed) toric principal bundles with given total equivariant characteristic class, as a locally closed subvariety of a product of partial flag varieties. This extends the construction of moduli of toric vector bundles by Sam Payne.