Poset embeddings of Hilbert functions and Betti numbers

JOURNAL OF ALGEBRA

卷:410

Article

Caviglia, Giulio¹  Kummini, Manoj² 

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[2] Chennai Math Inst, Siruseri 603103, Tamil Nadu, India

关键词: Graded Betti numbers;    Embeddings of Hilbert functions;    Hyperplane restriction theorems;    Lex-plus-powers conjecture;   

DOI  :  10.1016/j.jalgebra.2014.04.007

来源: Elsevier

【 摘 要 】

We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier by us in Caviglia and Kummini (2013) [5]. We show that if graded Betti numbers do not decrease when we replace ideals in an algebra by their embedded versions, then the same behaviour is carried over to ring extensions. As a corollary we give alternative inductive proofs of earlier results of Bigatti, Hulett, Pardue, Mermin, Peeva, Stillman and Mural. We extend a hypersurface restriction theorem of Herzog and Popescu to the situation of embeddings. We show that we can obtain the Betti table of an ideal in the extension ring from the Betti table of its embedded version by a sequence of consecutive cancellations. We further show that the lex-plus-powers conjecture of Evans reduces to the Artinian situation. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free