Abstract
Let \(S={\textsf {k}}[X_1,\dots , X_n]\) be a polynomial ring, where \({\textsf {k}}\) 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.
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Kumar, A., Kumar, R. Regularity, Rees algebra, and Betti numbers of certain cover ideals. Arch. Math. 115, 267–278 (2020). https://doi.org/10.1007/s00013-020-01486-9
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DOI: https://doi.org/10.1007/s00013-020-01486-9