Abstract
We introduce the notion of the twisted Segre product A∘ψB of Z-graded algebras A and B with respect to a twisting map ψ. It is proved that if A and B are noetherian Koszul Artin-Schelter regular algebras and ψ is a twisting map such that the twisted Segre product A∘ψB is noetherian, then A∘ψB 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∘ψB of A=k[u,v] and B=k[x,y] with respect to a diagonal twisting map ψ 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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