Title: On Maximal Primary Irreducible Ideals in $\F[x, y]$
Authors: Larry Smith (AG-Invariantentheorie) and R.E. Stong (University of Virginia)
Name of the .PDF file: rank\underscore two.pdf
}
At the beginning of the last century F.~S.~Macaulay developed an elegant
theory describing homogeneous ideals in polynomial rings. This theory
makes the maximal-primary irriducible ideals $I \subset \F[z_1\commadots
z_n]$ correspond to a single homogeneous inverse polynomial $\theta_I
\in \F[z_1^{-1} \commadots z_n^{-1}]$\/. Macaulay's theory has recently
attracted attention in connection with problems arising in invariant
theory and algebraic topology. In this note we show how given an
inverse binary form $\theta \in \F[x^{-1}, y^{-1}]$ one may explicitly
write down generators of the corresponding maximal-primary irreducible
ideal $I(\theta) \subset \F[x, y]$\/. As a bonus we obtain an
elementary proof of a theorem of Vasconcelos that such an ideal is
always generated by a regular sequence.