Sets of generators blocking all generators in finite classical polar spaces

TL;DR

This paper introduces generator blocking sets in finite classical polar spaces, generalizing maximal partial spreads, and characterizes minimal such sets in various polar spaces using cones with specific bases.

Contribution

It provides a new theoretical framework for understanding generator blocking sets and their minimal configurations in finite classical polar spaces.

Findings

Characterization of minimal generator blocking sets in Q(2n,q), Q-(2n+1,q), and H(2n,q^2)

Introduction of cones with vertices as subspaces within polar spaces

Generalization of maximal partial spreads to generator blocking sets

Abstract

We introduce generator blocking sets of finite classical polar spaces. These sets are a generalisation of maximal partial spreads. We prove a characterization of these minimal sets of the polar spaces Q(2n,q), Q-(2n+1,q) and H(2n,q^2), in terms of cones with vertex a subspace contained in the polar space and with base a generator blocking set in a polar space of rank 2.