Abstract
We consider orthogonal and symplectic analogues of determinantal varieties O ¯ r 1 , r 2 . Such varieties simultaneously generalize usual determinantal varieties and rank varieties of symmetric or anti-symmetric matrices. We find (non-minimal) resolutions of the coordinate rings of the varieties O ¯ r 1 , r 2 . We determine that “nearly all” such varieties are Cohen–Macaulay and for those that are Cohen–Macaulay we calculate the type. Furthermore, we provide a simple characterization for which varieties O ¯ r 1 , r 2 are Gorenstein. As an application, we present a class of ideals in k [ Hom ( E , F ) ] that are Gorenstein of codimension 4.
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