A Dirac structure lifts to the real projective blowup exactly for transverse submanifolds or invariant submanifolds whose transverse Lie algebras have constant height 0 or 1, classified as abelian, R semidirect R^n, or so(3).
Pure spinors on Lie groups
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Blowups of Dirac structures
A Dirac structure lifts to the real projective blowup exactly for transverse submanifolds or invariant submanifolds whose transverse Lie algebras have constant height 0 or 1, classified as abelian, R semidirect R^n, or so(3).