Tautological classes of hyper-K\"ahler manifolds. Erratum

TL;DR

This paper addresses a correction to a previous work on tautological classes of hyper-K"ahler manifolds, acknowledging a gap in the original proof and providing a partial recovery of the main results.

Contribution

It identifies a gap in the proof of a key theorem in the original paper and offers a partial correction, clarifying the impact on the main results.

Findings

Identified a gap in the original proof of Theorem 8.2.1.

Provided a partial recovery of the main results.

Clarified the limitations of the corrected proof.

Abstract

This note is an erratum to the paper "Tautological classes on moduli spaces of hyper-K\"ahler manifolds." Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of \cite[Theorem 8.2.1]{Duke}. We do not know how to correct the proof. We can only recover a partial statement. This gap affects the proof of one of the two main results of \cite{Duke}, we explain how to correct it.