On spinor varieties and their secants.
Manivel, Laurent (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Displaying similar documents to “Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties”
On spinor varieties and their secants.
Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
Frank Sottile (1999)
Colloquium Mathematicae
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We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.
Geometry of third order ODE systems
Alexandr Medvedev (2010)
Archivum Mathematicum
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We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application. ...
Variations of Hodge structure considered as an exterior differential system: old and new results.
Carlson, James, Green, Mark, Griffiths, Phillip (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Singularities of affine Schubert varieties.
Kuttler, Jochen, Lakshmibai, Venkatramani (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Integral canonical models of Shimura varieties
Mark Kisin (2009)
Journal de Théorie des Nombres de Bordeaux
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The aim of these notes is to provide an introduction to the subject of integral canonical models of Shimura varieties, and then to sketch a proof of the existence of such models for Shimura varieties of Hodge and, more generally, abelian type. For full details the reader is refered to [Ki 3].