Let denote an algebraically closed field. We study the relation between an ideal and its cross sections . In particular, we study under what conditions can be recovered from the set with . For instance, we show that an ideal , where is primary and , is uniquely determined by when . Moreover, there exists a function such that, if is generated by polynomials of degree at most~, then is uniquely determined by when . If is also known to be principal, the reconstruction can be made when , and in this case, we prove that the bound is sharp.
Cite this article
Martín Avendaño, Jorge Ortigas-Galindo, Interpolation of ideals. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 291–302DOI 10.4171/RMI/834