On deformations of hyperbolic varieties

Mario Kummer, Eli Shamovich

Research output: Contribution to journalArticlepeer-review


In this paper we study flat deformations of real subschemes of Pn, hyperbolic with respect to a fixed linear subspace, i.e., admit-ting a finite surjective and real fibered linear projection. We show that the subset of the corresponding Hilbert scheme consisting of such sub-schemes is closed and connected in the classical topology. Every smooth variety in this set lies in the interior of this set. Furthermore, we provide sufficient conditions for a hyperbolic subscheme to admit a flat deformation to a smooth hyperbolic subscheme. This leads to new examples of smooth hyperbolic varieties.

Original languageEnglish
Pages (from-to)593-612
Number of pages20
JournalMoscow Mathematical Journal
Issue number3
StatePublished - 1 Jul 2021


  • Deformations
  • Hilbert scheme
  • Hyperbolic variety

ASJC Scopus subject areas

  • General Mathematics


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