In this paper we study some cohomological properties of non-standard multigraded modules and Veronese transforms of them. Among others numerical characters, we study the generalized depth of a module and we see that it is invariant by taking a Veronese transform. We prove some vanishing theorems for the local cohomology modules of a multigraded module, as a corollary of these results we get that the depth of a Veronese module is asymptotically constant. © 2009.
Colomé-Nin, G., & Elias, J. (2009). Cohomological properties of non-standard multigraded modules. Journal of Algebra, 322(5), 1415–1429. https://doi.org/10.1016/j.jalgebra.2009.06.001