2002/06/14 by Johannes Huebschmann, Huebschmann, Johannes
Mathematics · #14L24 14L30 17B63 17B66 17B81 17C36 17C37 17C40 17C70 32C20 32Q15 32S05 32S60 53D17 53D20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG #msc:14L24 #msc:14L30 #msc:17B63 #msc:17B66 #msc:17B81 #msc:17C36 #msc:17C37 #msc:17C40 #msc:17C70 #msc:32C20 #msc:32Q15 #msc:32S05 #msc:32S60 #msc:53D17 #msc:53D20
paper · pdf · doi:10.48550/arxiv.math/0206143
AMSTEeX2.1, 11 pages
openalex publication_date 2002/06/14 · arxiv created 2004/01/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.