In this work, we study the Betti numbers of pinched Veronese rings, by means of the reduced homology of squarefree divisor complexes. We characterize when these rings are Cohen–Macaulay and we study the shape of the Betti tables for the pinched Veronese in the two variables. As a byproduct we obtain information on the linearity of such rings. Moreover, in the last section we compute the canonical modules of the Veronese modules.
"Cohen–Macaulay property and linearity of pinched Veronese rings." J. Commut. Algebra 13 (3) 347 - 360, Fall 2021. https://doi.org/10.1216/jca.2021.13.347