Abstract
We investigate the $x$- and $y$-regularity of a bigraded $K$-algebra $R$ as introduced in \cite{ARCRNE}. These notions are used to study asymptotic properties of certain finitely generated bigraded modules. As an application we get for any equigenerated graded ideal $I$ upper bounds for the number $j_0$ for which $\operatorname{reg}(I^j)$ is a linear function for $j \geq j_0$. Finally, we give upper bounds for the $x$- and $y$-regularity of generalized Veronese algebras.
Citation
Tim Römer. "Homological properties of bigraded algebras." Illinois J. Math. 45 (4) 1361 - 1376, Winter 2001. https://doi.org/10.1215/ijm/1258138072
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