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- W2271875500 abstract "A monomial ideal $I$ admits a Betti splitting $I=J+K$ if the Betti numbers of $I$ can be determined in terms of the Betti numbers of the ideals $J,K$ and $J cap K$. Given a monomial ideal $I$, we prove that $I=J+K$ is a Betti splitting of $I$, provided $J$ and $K$ are componentwise linear, generalizing a result of Francisco, H`a and Van Tuyl. If $I$ has a linear resolution, the converse also holds. We apply this result recursively to the Alexander dual of vertex-decomposable, shellable and constructible simplicial complexes and to determine the graded Betti numbers of the defining ideal of three general fat points in the projective space." @default.
- W2271875500 created "2016-06-24" @default.
- W2271875500 creator A5084224233 @default.
- W2271875500 date "2014-10-23" @default.
- W2271875500 modified "2023-09-27" @default.
- W2271875500 title "Betti splitting via componentwise linear ideals" @default.
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