Severi varieties and holomorphic nilpotent orbits

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Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective space; the cubic and projective space are identified in terms of holomorphic nilpotent orbits. The projective space acquires an exotic Kähler structure with three strata, the cubic is an example of an exotic projective variety with two strata, and the corresponding Severi variety is the closed stratum in the exotic variety as well as in the exotic projective space. In the standard cases, these varieties arise also via Kähler reduction. An interpretation in terms of constrained mechanical systems is included.
AMSTEeX2.1, 11 pages

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Differential Geometry, Symplectic Geometry, 14L24 14L30 17B63 17B66 17B81 17C36 17C37 17C40 17C70 32C20 32Q15 32S05 32S60 53D17 53D20

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http://salesiana.dossiersoluciones.com/handle/123456789/64301

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206143
 http://arxiv.org/abs/math/0206143

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arXiv