On the Weak Lefschetz Property for artinian Gorenstein algebras of codimension three

• We study the problem of whether an arbitrary codimension three graded artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this problem to checking whether it holds for all compressed Gorenstein algebras of odd socle degree. In the first open case, namely Hilbert function (1, 3, 6, 6, 3, 1), we give a complete answer in every characteristic by translating the problem to one of studying geometric aspects of certain morphisms from P2 to P3, and Hesse configurations in P2.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Artinian algebra

Gorenstein algebra

Hesse configuration

Primary

Secondary

Weak Lefschetz Property

Publication and Content Type

ref (subject category)

art (subject category)