Curves Arising from Endomorphism Rings of Kronecker Modules

David McKinnon, Mike Roth
2007 Rocky Mountain Journal of Mathematics  
In this note, we prove that the endomorphism ring of a Kronecker module attached to a power series α ∈ k[[X]] is minimally generated by three generators, unless its degree d is less than 3. We prove this via the theory of algebraic curves, by proving that none of the affine curves arising from these endomorphism rings are planar for d ≥ 3, but can always be embedded in A 3 .
doi:10.1216/rmjm/1182536167 fatcat:23mwjao4n5dv3alccucn7menb4