Singular Poisson-Kaehler geometry of Scorza varieties and their secant varieties

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dc.creatorHuebschmann, Johannes
dc.date2004-05-10
dc.date.accessioned2026-07-07T07:36:58Z
dc.date.available2026-07-07T07:36:58Z
dc.descriptionEach Scorza variety and its secant varieties in the ambient projective space are identified, in the realm of singular Poisson-Kaehler geometry, in terms of projectivizations of holomorphic nilpotent orbits in suitable Lie algebras of hermitian type, the holomorphic nilpotent orbits, in turn, being affine varieties. The ambient projective space acquires an exotic Kaehler structure, the closed stratum being the Scorza variety and the closures of the higher strata its secant varieties. In this fashion, the secant varieties become exotic projective varieties. In the rank 3 case, the four regular Scorza varieties coincide with the four critical Severi varieties. In the standard cases, the Scorza varieties and their secant varieties arise also via Kaehler reduction. An interpretation in terms of constrained mechanical systems is included.
dc.descriptionAMSTeX2.1, 16 pages
dc.identifierhttps://arxiv.org/abs/math/0405165
dc.identifierhttp://arxiv.org/abs/math/0405165
dc.identifierDifferential Geometry and its Applications 23 (2005) 79-93
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120613
dc.subjectSymplectic Geometry
dc.subjectAlgebraic Geometry
dc.subject14L24 14L30 17B63 17B66 17B81 17C36 17C40 17C70 32C20 32Q15 32S05 32S60 53C30 53D17 53D20
dc.titleSingular Poisson-Kaehler geometry of Scorza varieties and their secant varieties
dc.typetext

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