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

We study a generalization of Nagata idealization for level algebras. Thesealgebras are standard graded Artinian algebras whose Macaulay dual generator isgiven explicity as a bigraded polynomial of bidegree $(1,d)$. We consider thealgebra associated to polynomials of the same type of bidegree $(d_1,d_2)$. Weprove that the geometry of the Nagata hypersurface of order $e$ is very similarto the geometry of the original hypersurface. We study the Lefschetz propertiesfor Nagata idealizations of order $e$, proving that WLP holds if $d_1\geq d_2$.We give a complete description of the associated algebra in the monomial squarefree case.

Lefschetz Properties for Higher Order Nagata Idealizations