Cohomology of 3-points configuration spaces of complex projective spaces

TL;DR

This paper calculates the Betti numbers and cohomology algebras of configuration spaces of three points in complex projective spaces, including special cases like collinear points and the infinite-dimensional scenario.

Contribution

It provides explicit cohomological invariants for three-point configuration spaces in complex projective spaces, extending to infinite dimensions and special geometric arrangements.

Findings

Betti numbers for ordered and unordered configuration spaces computed

Cohomology algebras described explicitly

Results include infinite-dimensional cases and special point arrangements

Abstract

We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for the configuration spaces of three collinear and non-collinear points.