2009/10/20 by Lucian Bădescu, Badescu, Lucian, Giuseppe Valla +1
Computer Science · Engineering · Mathematics · #14B20 #14M12 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0910.3847
openalex publication_date 2009/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the Grothendieck-Lefschetz theory (see \cite[SGA2]) we prove a criterion to deduce that certain subvarieties of \mathbb Pn of dimension ≥ 2 are not set-theoretic complete intersections (see Theorem 1 of the Introduction). As applications we give a number of relevant examples. In the last part of the paper we prove that the arithmetic rank of a rational normal d-dimensional scroll Sn1,...,nd in \mathbb PN is N-2, by producing an explicit set of N-2 homogeneous equations which define these scrolls set-theoretically (see Theorem 2 of the Introduction).