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It is well known in literature about the determinantal varieties, symmetric determinantal varities, skew-symmetric determinantal varieties. Is it possible to study determinantal varieties over the set of hermitian matrices? Is there any study about the hermitian determinantal varieties? I have no idea about the geometry so, it may be a non sense question. If it is the case, I am sorry for that in advance.

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  • $\begingroup$ You might be interested in this answer : mathoverflow.net/questions/318968/… where the slightly more difficult case of hermitian matrices with quaternionic coefficients is dealt with. $\endgroup$
    – Libli
    Commented Dec 21, 2022 at 19:12

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