Lefschetz Properties for Higher Order Nagata Idealizations

Armando Cerminara; Rodrigo Gondim; Giovanna Ilardi; Fulvio Maddaloni

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arXiv · 1807.06415

Lefschetz Properties for Higher Order Nagata Idealizations

Armando Cerminara·Rodrigo Gondim·Giovanna Ilardi·Fulvio Maddaloni

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Abstract

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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BibTeX RIS

Armando Cerminara, Rodrigo Gondim, Giovanna Ilardi, Fulvio Maddaloni. 2018-07-17. Lefschetz Properties for Higher Order Nagata Idealizations. https://arxiv.org/abs/1807.06415

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