arXiv subjects
Publications and source records attributed to S. L'vovsky.
Generalizing a classical lemma of Castelnuovo, we characterize rational normal curves (resp. linearly normal elliptic curves) as curves $C\subset \PP^n$ such that the number of linearly independent hypersurfaces $Z\supset C$ of given degree~$m$ is maximal (resp. next to maximal).
In his preprint ``Differential-Geometric Characterizations of Complete Intersections'' (alg-geom/9407002), J.M.Landsberg introduces an elementary characterization of complete intersections. The proof of this criterion uses the method of moving frames. The aim of this note is to present an elementary proof of Landsberg's criterion that is valid over any ground field.
In this paper we describe projective curves and surfaces such that almost all their hyperplane sections are projectively equivalent. Our description is complete for curves and close to being complete for smooth surfaces. In the appendix we make some remarks on connections between the mentioned property of a projective variety and its adjunction properties.