Mathematics > Algebraic Geometry
[Submitted on 17 Jul 2018 (v1), last revised 12 Feb 2019 (this version, v2)]
Title:Lefschetz Properties for Higher Order Nagata Idealizations
View PDFAbstract:We study a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicity as a bigraded polynomial of bidegree $(1,d)$. We consider the algebra associated to polynomials of the same type of bidegree $(d_1,d_2)$. We prove that the geometry of the Nagata hypersurface of order $e$ is very similar to the geometry of the original hypersurface. We study the Lefschetz properties for 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 square free case.
Submission history
From: Armando Cerminara [view email][v1] Tue, 17 Jul 2018 13:33:30 UTC (20 KB)
[v2] Tue, 12 Feb 2019 11:21:11 UTC (20 KB)
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