Geodesic
Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties
Archivum mathematicum, Tome 44 (2008) no. 5, pp. 419-447.

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These are expository notes from the 2008 Srní Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
Classification : 14M17, 53A20, 53C30
Keywords: projective rigidity; exterior differential systems; Lie algebra cohomology; homogeneous varieties 
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Landsberg, Joseph M. Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties. Archivum mathematicum, Tome 44 (2008) no. 5, pp. 419-447. http://geodesic.mathdoc.fr/item/ARM_2008__44_5_a7/