Linear factorization of binary forms and its correspondence to the vanishing of covariants

DOI: 10.5176/2251-3388_1.1.1

Authors: Pamini Thangarajah

Abstract:

In this paper we study the topological properties of the following set : For a given partition (m1; : : : ;ms) of a positive integer r; the set of binary forms f of degree r in the variables X0;X1 over the field of complex numbers C such that f has the form lm11 : : : lmss for some linear forms l1; : : : ; ls;. Also,we will explore the covariant generators for the corresponding prime ideal of this set.

Keywords: Zariski closed sets, binary forms, covariants,invariants