Togliatti systems associated to the dihedral group and the weak Lefschetz property

2021/01/24 by Liena Colarte-Gómez, Colarte-Gómez, Liena, Emilia Mezzetti +5
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.2101.09687

To appear in Israel Journal of Mathematics

arxiv created 2021/01/24 · arxiv updated 2021/01/26

Abstract

In this note, we study Togliatti systems generated by invariants of the dihedral group D_2d acting on k[x₀,x₁,x₂]. This leads to the first family of non monomial Togliatti systems, which we call GT-systems with group D_2d. We study their associated varieties S_D_2d, called GT-surfaces with group D_2d. We prove that they are arithmetically Cohen-Macaulay surfaces whose homogeneous ideal, I(S_D_2d), is minimally generated by quadrics and we find a minimal free resolution of I(S_D_2d).

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