arXiv subjects

Junzo Watanabe

Publications and source records attributed to Junzo Watanabe.

21 records · Page 2Linked to original sources

arXiv2012

The weak Lefschetz property for m-full ideals and componentwise linear ideals

We give a necessary and sufficient condition for a standard graded Artinian ring defined by an m-full ideal, to have the weak Lefschetz property in terms of graded Betti numbers. This is a generalization of a theorem of Wiebe for componentwise linear ideals. We also prove that the class of componentwise linear ideals and that of completely m-full ideals coincide in characteristic zero and in positive characteristic, with the assumption that the generic initial ideal w.r.t. the graded reverse lexicographic order is stable.

math.AC↗

arXiv2009

Lefschetz elements of Artinian Gorenstein algebras and Hessians of homogeneous polynomials

We give a characterization of the Lefschetz elements in Artinian Gorenstein rings over a field of characteristic zero in terms of the higher Hessians. As an application, we give new examples of Artinian Gorenstein rings which do not have the strong Lefschetz property.

math.AC↗

arXiv2007

The strong Lefschetz property for Artinian algebras with non-standard grading

We define the strong Lefschetz property for finite graded modules over graded Artinian algebras whose grading is not necessarily standard. We show that most results which have been obtained for Artinian algebras with standard grading can be extended for non-standard grading. Our results on the strong Lefschetz property for non-standard grading can be used to prove that certain Artinian complete intersections with standard grading have the strong Lefschetz property.

math.AC↗