2024/04/30 by Jun-Muk Hwang, Hwang, Jun-Muk
Computer Science · #14M15 #53A20 #53D10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2404.19376
openalex publication_date 2024/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a symplectic vector space V, a projective subvariety Z ⊂ \bf P V is a Legendrian variety if its affine cone \widehatZ ⊂ V is Lagrangian. In addition to the classical examples of subadjoint varieties associated to simple Lie algebras, many examples of nonsingular Legendrian varieties have been discovered which have positive-dimensional automorphism groups. We give a characterization of subadjoint varieties among such Legendrian varieties in terms of the isotropy representation. Our proof uses some special features of the projective third fundamental forms of Legendrian varieties and their relation to the lines on the Legendrian varieties.