Regularity, Rees algebra and Betti numbers of certain cover ideals

Abstract

Let $S=\mathsf{k}[X_1,\dots ,X_n]$ be a polynomial ring, where $\mathsf{k}$ is a field. This article deals with the defining ideal of the Rees algebra of squarefree monomial ideal generated in degree $n-2$. As a consequence, we prove that Betti numbers of powers of the cover ideal of the complement graph of a tree do not depend on the choice of tree. Further, we study the regularity and Betti numbers of powers of cover ideals associated to certain graphs.

Title has been changed and some new result has been added. To be appear in Archiv Der Mathematik

References in corpus (1)

• Homological properties of bigraded algebras