Betti splitting via componentwise linear ideals

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• 作者：Davide Bolognini ^{bolognin@dima.unige.it" class="auth_mail" title="E-mail the corresponding author davide.bolognini@yahoo.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13D02 ; 13A02 ; secondary ; 05E40 ; 05E45
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：455
• 期：Complete
• 页码：1-13
• 全文大小：349 K

文摘

A monomial ideal I   admits a Betti splitting 11dc337a9088" title="Click to view the MathML source">I=J+K$I=J+K$ if the Betti numbers of I can be determined in terms of the Betti numbers of the ideals J, K   and J∩K$J\cap K$. Given a monomial ideal I  , we prove that 11dc337a9088" title="Click to view the MathML source">I=J+K$I=J+K$ is a Betti splitting of I, provided J and K are componentwise linear, generalizing a result of Francisco, Hà 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. Moreover we determine the graded Betti numbers of the defining ideal of three general fat points in the projective space.