Grothendieck-Lefschetz Theory, Set-Theoretic Complete Intersections and Rational Normal Scrolls - Mathematics > Algebraic GeometryReport as inadecuate




Grothendieck-Lefschetz Theory, Set-Theoretic Complete Intersections and Rational Normal Scrolls - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: Using the Grothendieck-Lefschetz theory see \cite{SGA2} we prove acriterion to deduce that certain subvarieties of $\mathbb P^n$ of dimension$\geq 2$ are not set-theoretic complete intersections see Theorem 1 of theIntroduction. As applications we give a number of relevant examples. In thelast part of the paper we prove that the arithmetic rank of a rational normal$d$-dimensional scroll $S {n 1,

.,n d}$ in $\mathbb P^N$ is $N-2$, byproducing an explicit set of $N-2$ homogeneous equations which define thesescrolls set-theoretically see Theorem 2 of the Introduction.



Author: Lucian Badescu, Giuseppe Valla

Source: https://arxiv.org/



DOWNLOAD PDF




Related documents