Flocks of Cones: Star Flocks

TL;DR

This paper generalizes the concept of star flocks from quadratic cones to arbitrary cones, classifies them using minimal blocking sets, and provides new examples of bilinear flocks for non-quadratic cones.

Contribution

It introduces a generalization of star flocks to arbitrary cones and establishes a classification method via minimal blocking sets, also producing new bilinear flock examples.

Findings

Star flocks can be classified using minimal blocking sets of Redei type.

The concept of star flocks extends beyond quadratic cones to arbitrary cones.

New examples of bilinear flocks for non-quadratic cones are constructed.

Abstract

The concept of a flock of a quadratic cone is generalized to arbitrary cones. Flocks whose planes contain a common point are called star flocks. Star flocks can be described in terms of their coordinate functions. If the cone is "big enough", the star flocks it admits can be classified by means of a connection with minimal blocking sets of Redei type. This connection can also be used to obtain examples of bilinear flocks of non-quadratic cones.