TY - JOUR
T1 - On the Weak Lefschetz Property for artinian Gorenstein algebras of codimension three
AU - Boij, Mats
AU - Migliore, Juan
AU - Miró-Roig, Rosa M.
AU - Nagel, Uwe
AU - Zanello, Fabrizio
PY - 2014/2/1
Y1 - 2014/2/1
N2 - 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.
AB - 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.
KW - Artinian algebra
KW - Gorenstein algebra
KW - Hesse configuration
KW - Primary
KW - Secondary
KW - Weak Lefschetz Property
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U2 - 10.1016/j.jalgebra.2014.01.003
DO - 10.1016/j.jalgebra.2014.01.003
M3 - Article
AN - SCOPUS:84893155346
SN - 0021-8693
VL - 403
SP - 48
EP - 68
JO - Journal of Algebra
JF - Journal of Algebra
ER -