Abstract
In this note, we study Togliatti systems generated by invariants of the dihedral group D2d acting on k[x0, x1, x2]. This leads to the first family of non-monomial Togliatti systems, which we call GT-systems with group D2d. We study their associated varieties \({S_{{D_{2d}}}}\), called GT-surfaces with group D2d. We prove that there 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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