Let F be the family of graded ideals J in the exterior algebra E of a n-dimensional vector space over a field K such that e(E/J) = dim(K) (E/J) = e, indeg (E/J) = i and H-E/J (i) = dim(K) (E/J)(i) are fixed integers. It is shown that there exists a unique lexsegment graded ideal J(n, e, i) is an element of F whose Betti numbers give an upper bound for the Betti numbers of the ideals of F. The authors continue the computation of upper bounds for the Betti numbers of graded ideals with given data started in Crupi and Utano (1999).

Classes of graded ideals with given data in the exterior algebra

CRUPI, Marilena;UTANO, Rosanna
2007

Abstract

Let F be the family of graded ideals J in the exterior algebra E of a n-dimensional vector space over a field K such that e(E/J) = dim(K) (E/J) = e, indeg (E/J) = i and H-E/J (i) = dim(K) (E/J)(i) are fixed integers. It is shown that there exists a unique lexsegment graded ideal J(n, e, i) is an element of F whose Betti numbers give an upper bound for the Betti numbers of the ideals of F. The authors continue the computation of upper bounds for the Betti numbers of graded ideals with given data started in Crupi and Utano (1999).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1682082
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