English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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).

Grothendieck-Lefschetz Theory, Set-Theoretic Complete Intersections and Rational Normal Scrolls