Seminar in Algebraic Geometry and Number Theory

Abstract: We study a two-parameter family of non-standard graded complete intersection algebras A(m,n). In 1989, Almkvist conjectures that the Hilbert function of A(m,n) is unimodal for n odd and sufficiently large m, and for n even and any m. Since unimodality is a necessary condition for Lefschetz properties, we study these properties and prove that the conjecture holds for n=2.