Resumen de A finite classification of (x, y)-primary ideals of low multiplicity

Paolo Mantero, Jason McCullough

• Let S be a polynomial ring over an algebraically closed field k. Let x and y denote linearly independent linear forms in S so that {\mathfrak {p}}= (x,y) is a height two prime ideal. This paper concerns the structure of {\mathfrak {p}}-primary ideals in S. Huneke, Seceleanu, and the authors showed that for e \ge 3, there are infinitely many pairwise non-isomorphic {\mathfrak {p}}-primary ideals of multiplicity e. However, we show that for e \le 4 there is a finite characterization of the linear, quadric and cubic generators of all such {\mathfrak {p}}-primary ideals. We apply our results to improve bounds on the projective dimension of ideals generated by three cubic forms.