Normality of Rees algebras of generalized mixed product ideals

Year 2024, Volume: 35 Issue: 35, 168 - 185, 09.01.2024

Monica La Barbıera Roya Moghımıpor

https://doi.org/10.24330/ieja.1402961

Abstract

Let $K$ be a field and $K[x_1,x_{2}]$ the polynomial ring in two
variables over $K$ with each $x_i$ of degree $1$. Let $L$ be the
generalized mixed product ideal induced by a monomial ideal
$I\subset K[x_1,x_2]$, where the ideals substituting the monomials
in $I$ are squarefree Veronese ideals. In this paper, we study the
integral closure of $L$, and the normality of $\mathcal{R}(L)$, the
Rees algebra of $L$. Furthermore, we give a geometric description of
the integral closure of $\mathcal{R}(L)$.

Keywords

Integral closure, normality, Rees algebra, generalized mixed product ideal

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