Orbits of linear series on the projective line

TL;DR

This paper computes the equivariant fundamental class of orbit closures of linear series on the projective line, describing their boundaries and specializations within one-parameter families.

Contribution

It provides explicit calculations of orbit closure classes and analyzes boundary structures and degenerations of linear series on the projective line.

Findings

Explicit formulas for equivariant fundamental classes

Description of boundary components of orbit closures

Analysis of orbit degenerations in families

Abstract

We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits specialise in one parameter families.