Griffiths-Harris rigidity of compact Hermitian symmetric spaces
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I prove that any complex manifold that has a projective second fundmental form isomorphic to one of a rank two compact Hermitian symmetric space (other than a quadric hypersurface) at a general point must be an open subset of such a space. This contrasts the non-rigidity of all other compact Hermitian symmetric spaces observed in [12, 13]. A key step is the use of higher order Bertini type theorems that may be of interest in their own right. 2006 Applied Probability Trust.
JOURNAL OF DIFFERENTIAL GEOMETRY
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