A point of the intersection of two quadrics is very stable exactly when the polynomial p(z) built from its coordinates has distinct roots.
Hausel, Enhanced mirror symmetry for Langlands dual Hitchin systems , Pro- ceedings of ICM 2022, 2228–2249
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Remarks on the intersection of two quadrics
A point of the intersection of two quadrics is very stable exactly when the polynomial p(z) built from its coordinates has distinct roots.