On equations defining coincident root loci

TL;DR

This paper investigates algebraic conditions on binary form coefficients to ensure roots with specified multiplicities, contributing to the understanding of coincident root loci in algebraic geometry.

Contribution

It introduces new algebraic conditions characterizing binary forms with roots of predetermined multiplicities, advancing the theory of coincident root loci.

Findings

Derived explicit algebraic conditions for coincident root loci

Provided a framework for identifying forms with prescribed root multiplicities

Enhanced understanding of the structure of algebraic conditions in root multiplicity problems

Abstract

We study the problem of specifying algebraic conditions on the coefficients of a binary form, so that it may have roots with preassigned multiplicities.