A remark on extremal stability of configuration spaces

TL;DR

This paper investigates the extremal stability of configuration spaces in complex projective spaces, demonstrating homology vanishing in the extremal stable range and confirming a conjecture by Knudsen, Miller, and Tosteson.

Contribution

It provides an explicit analysis of extremal stability in complex projective configuration spaces and confirms a previously open question.

Findings

Homology groups vanish in the extremal stable range.

Affirmative answer to Knudsen, Miller, and Tosteson's question.

Abstract

We explicitly study the extremal stability of configuration spaces of complex projective spaces of any dimension, and show that the homology groups are vanish in extremal stable range. As a consequence, we give an affirmative answer of the question of Knudsen, Miller and Tosteson.