Corrigendum to `Orbit closures in the enhanced nilpotent cone', published in Adv. Math. 219 (2008)

TL;DR

This paper corrects an error in a previous work on orbit closures in the enhanced nilpotent cone, providing independent proofs to ensure the validity of subsequent results.

Contribution

It identifies and rectifies a proof error regarding affine pavings in orbit closure resolutions, reaffirming the validity of related results.

Findings

Correction of the proof error in Theorem 4.7

Independent proofs of subsequent dependent results

Validation of the overall results despite the correction

Abstract

In this note, we point out an error in the proof of Theorem 4.7 of [P. Achar and A.~Henderson, `Orbit closures in the enhanced nilpotent cone', Adv. Math. 219 (2008), 27-62], a statement about the existence of affine pavings for fibres of a certain resolution of singularities of an enhanced nilpotent orbit closure. We also give independent proofs of later results that depend on that statement, so all other results of that paper remain valid.