Iterated multiple points I: functoriality, defining equations and pathologies

TL;DR

This paper investigates the properties of Kleiman's iterated multiple point spaces, providing explicit equations for their description and discussing issues related to dimension and symmetry pathologies.

Contribution

It introduces general properties of iterated multiple point spaces and derives explicit equations for maps between complex manifolds, addressing their structural complexities.

Findings

Explicit equations for multiple point spaces of any corank

Identification of dimension-related pathologies

Discussion of symmetry-related issues in these spaces

Abstract

This is the first of a two-part work on Kleiman's iterated multiple point spaces. We show general properties of these spaces, leading to explicit equations describing them for maps (of any corank) between complex manifolds. We also describe pathologies regarding dimension and lack of symmetry