Twisted Segre products

We introduce the notion of the twisted Segre product A o psi B of 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 o psi B is noetherian, then A o 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 o 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. (c) 2022 Elsevier Inc. All rights reserved. <comment>Superscript/Subscript Available</comment