Resumen de Interpolation of ideals

Martín Avendaño , Jorge Ortigas Galindo

• 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.