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- Hokkaido UniversityJP22 papers
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8 papers · 1 filter
Lefschetz properties for complete intersection ideals generated by products of linear forms
Martina Juhnke-Kubitzke, Rosa M. Miró-Roig, Satoshi Murai +1
In this paper, we study the strong Lefschetz property of artinian complete intersection ideals generated by products of linear forms. We prove the strong Lefschetz property for a c…
A characterization of the Macaulay dual generators for quadratic complete intersections
Tadahito Harima, Akihito Wachi, Junzo Watanabe
Let be a homogeneous polynomial in variables of degree over a field . Let be the associated Artinian graded -algebra. If is a subalgebra o…
The EGH Conjecture and the Sperner property of complete intersections
Tadahito Harima, Akihito Wachi, Junzo Watanabe
Let be a graded complete intersection over a field and the monomial complete intersection with the generators of the same degrees as . The EGH conjecture says that if $I…
The commutator algebra of a nilpotent matrix and an application to the theory of commutative Artinian algebras
Tadahito Harima, Junzo Watanabe
We show a number of properties of the commutator algebra of a nilpotent matrix over a field. In particular we determine the simple modules of the commutator algebra. Then the resul…
Generic initial ideals of some monomial complete intersections in four variables
Tadahito Harima, Sho Sakaki, Akihito Wachi
Let be the polynomial ring over a field of characteristic zero. For the ideal , where at least one of , ,…
Generic initial ideals, graded Betti numbers and -Lefschetz properties
Tadahito Harima, Akihito Wachi
We introduce the -strong Lefschetz property (-SLP) and the -weak Lefschetz property (-WLP) for graded Artinian -algebras, which are generalizations of the Lefschetz…