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arXiv · 2111.04245

Twisted Segre products

Ji-Wei He·Kenta Ueyama
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Abstract

We introduce the notion of the twisted Segre product $A\circ_\psi B$ of $\mathbb Z$-graded algebras $A$ and $B$ with respect to a twisting map $\psi$. It is proved that if $A$ and $B$ are noetherian Koszul Artin-Schelter regular algebras and $\psi$ is a twisting map such that the twisted Segre product $A\circ_\psi B$ is noetherian, then $A\circ_\psi B$ is a noncommutative graded isolated singularity. To prove this result, the notion of densely (bi-)graded algebras is introduced. Moreover, we show that the twisted Segre product $A\circ_\psi B$ of $A=k[u,v]$ and $B=k[x,y]$ with respect to a diagonal twisting map $\psi$ is a noncommutative quadric surface (so in particular it is noetherian), and we compute the stable category of graded maximal Cohen-Macaulay modules over it.

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Ji-Wei He, Kenta Ueyama. 2021-11-08. Twisted Segre products. https://arxiv.org/abs/2111.04245

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