Lefschetz Properties for Higher Order Nagata Idealizations

Lefschetz Properties for Higher Order Nagata Idealizations

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_...

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Hauptverfasser: Cerminara, Armando, Gondim, Rodrigo, Ilardi, Giovanna, Maddaloni, Fulvio
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Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
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Gondim, Rodrigo
Ilardi, Giovanna
Maddaloni, Fulvio
description 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.
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Mathematics - Commutative Algebra
title Lefschetz Properties for Higher Order Nagata Idealizations
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