Regularity, Rees algebra, and Betti numbers of certain cover ideals

Abstract

Let S= k[X1, ⋯ , Xn] be a polynomial ring, where k is a field. This article deals with the defining ideal of the Rees algebra of a 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 the tree. Further, we study the regularity and Betti numbers of powers of cover ideals associated to certain graphs. © 2020, Springer Nature Switzerland AG.