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Given a complex submanifold $M $ of the projective space $ \mathbb P(T)$,the hyperplane system $R$ on $M$ characterizes the projective embedding of $M$ into $\mathbb P(T)$ in the following sense: for any two nondegenerate complex submanifolds $M \subset \mathbb P(T)$ and $M '\subset \mathbb P(T')$, there is a projective linear transformation that sends an open subset of $M$ onto an open subset of $M'$ if and only if $(M, R)$ is locally equivalent to $(M', R')$. Se-ashi developed a theory for the differential invariants of these types of systems of linear differential equations. In particular, the theory applies to systems of linear differential equations that have symbols equivalent to the hyperplane systems on nondegenerate equivariant embeddings of compact Hermitian symmetric spaces. In this paper, we extend this result to hyperplane systems on nondegenerate equivariant embeddings of homogeneous spaces of the first kind.
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참고문헌 (12)
참고문헌 신청
B. Pasquier / 2009 / On some smooth projective two-orbit varieties with Picard number 1 / Math. Ann 344 (4) : 963 ~ 987
D. N. Akhiezer / 1983 / Equivariant completions of homogeneous algebraic varieties by homo-geneous divisors / Ann. Global Anal. Geom 1 (1) : 49 ~ 78
D. N. Akhiezer / 1995 / Lie group actions in complex analysis, Aspects of Mathematics, E27 / Vieweg and Sohn
J. -M. Hwang / 2003 / Characterization of Hermitian symmetric spaces by fundamental forms / Duke Math. J 120 (3) : 621 ~ 634
J. M. Landsberg / 1999 / On the infinitesimal rigidity of homogeneous varieties / Compositio Math 118 (2) : 189 ~ 201
D. N. Akhiezer / 1983 / Equivariant completions of homogeneous algebraic varieties by homo-geneous divisors / Ann. Global Anal. Geom 1 (1) : 49 ~ 78
D. N. Akhiezer / 1995 / Lie group actions in complex analysis, Aspects of Mathematics, E27 / Vieweg and Sohn
J. -M. Hwang / 2003 / Characterization of Hermitian symmetric spaces by fundamental forms / Duke Math. J 120 (3) : 621 ~ 634
J. M. Landsberg / 1999 / On the infinitesimal rigidity of homogeneous varieties / Compositio Math 118 (2) : 189 ~ 201
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