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

• Autores: Paolo Mantero, Jason McCullough
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 69, Fasc. 1, 2018, págs. 107-130
• Idioma: inglés
• DOI: 10.1007/s13348-017-0196-4
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• Resumen

  • 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 ?=(?,?) is a height two prime ideal. This paper concerns the structure of ? -primary ideals in S. Huneke, Seceleanu, and the authors showed that for ?≥3 , there are infinitely many pairwise non-isomorphic ? -primary ideals of multiplicity e. However, we show that for ?≤4 there is a finite characterization of the linear, quadric and cubic generators of all such ? -primary ideals. We apply our results to improve bounds on the projective dimension of ideals generated by three cubic forms.