Abstract
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 language | English |
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Pages (from-to) | 593-612 |
Number of pages | 20 |
Journal | Moscow Mathematical Journal |
Volume | 21 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jul 2021 |
Keywords
- Deformations
- Hilbert scheme
- Hyperbolic variety
ASJC Scopus subject areas
- General Mathematics