Subspace arrangements, configurations of linear spaces and the quadrics containing them

TL;DR

This paper investigates the quadratic components of the ideals of subspace arrangements and linear space configurations, providing explicit Hilbert function calculations for generic cases.

Contribution

It determines the Hilbert function in degree 2 for generic configurations of linear spaces, advancing understanding of their algebraic properties.

Findings

Explicit Hilbert function HF(L,2) for generic configurations

Characterization of quadrics containing subspace arrangements

Enhanced understanding of algebraic structure of linear space configurations

Abstract

A subspace arrangement in a vector space is a finite collection of vector subspaces. Similarly, a configuration of linear spaces in a projective space is a finite collection of linear subspaces. In this paper we study the degree 2 part of the ideal of such objects. More precisely, for a generic configuration of linear spaces L we determine HF(L,2), i.e. the Hilbert function of L in degree 2.