Interpolation of ideals

• Martín Avendaño ^[1] ; Jorge Ortigas Galindo ^[1]
  1. [1] Academia General Militar
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 1, 2015, págs. 291-302
• Idioma: inglés
• DOI: 10.4171/RMI/834
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let K denote an algebraically closed field. We study the relation between an ideal I⊆K[x1,…,xn] and its cross sections Iα=I+⟨x1−α⟩. In particular, we study under what conditions I can be recovered from the set IS={(α,Iα):α∈S} with S⊆K. For instance, we show that an ideal I=⋂iQi, where Qi is primary and Qi∩K[x1]={0}, is uniquely determined by IS when |S|=∞. Moreover, there exists a function B(δ,n) such that, if I is generated by polynomials of degree at most~δ, then I is uniquely determined by IS when |S|≥B(δ,n). If I is also known to be principal, the reconstruction can be made when |S|≥2δ, and in this case, we prove that the bound is sharp.