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arXiv · 2005.01501

CW-complex Nagata Idealizations

Armando Capasso·Pietro De Poi·Giovanna Ilardi
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Abstract

We introduce a novel construction which allows us to identify the elements of the skeletons of a CW-complex $P(m)$ and the monomials in $m$ variables. From this, we infer that there is a bijection between finite CW-subcomplexes of $P(m)$, which are quotients of finite simplicial complexes, and some bigraded standard Artinian Gorenstein algebras, generalizing previous constructions in \cite{F:S}, \cite{CGIM} and \cite{G:Z}. We apply this to a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a bigraded polynomial of bidegree $(1,d)$. We consider the algebra associated to polynomials of the same type of bidegree $(d_1,d_2)$.

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Armando Capasso, Pietro De Poi, Giovanna Ilardi. 2020-05-04. CW-complex Nagata Idealizations. https://doi.org/10.1016/j.aam.2020.102079

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