A Nullstellensatz for Łojasiewicz ideals

  • Francesca Acquistapace

    Università degli Studi di Pisa, Italy
  • Fabrizio Broglia

    Università degli Studi di Pisa, Italy
  • Andreea Nicoara

    University of Pennsylvania, Philadelphia, USA


For an ideal of smooth functions a\mathfrak a that is either Łojasiewicz or weakly Łojasiewicz, we give a complete characterization of the ideal of functions vanishing on its variety I(Z(a))\mathcal I(\mathcal Z (\mathfrak a)) in terms of the global Łojasiewicz radical and Whitney closure. We also prove that the Łojasiewicz radical of such an ideal is analytic-like in the sense that its saturation equals its Whitney closure. This allows us to revisit Nullstellensatz results due to Bochnak and Adkins–Leahy and to resolve positively a modification of the Nullstellensatz conjecture due to Bochnak.

Cite this article

Francesca Acquistapace, Fabrizio Broglia, Andreea Nicoara, A Nullstellensatz for Łojasiewicz ideals. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1479–1487

DOI 10.4171/RMI/822