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Characterizing subadjoint varieties among Legendrian varieties
- Publication Year :
- 2024
-
Abstract
- For a symplectic vector space $V$, a projective subvariety $Z \subset {\bf P} V$ is a Legendrian variety if its affine cone $\widehat{Z} \subset V$ 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.<br />Comment: to appear in Ann. Inst. Fourier (Grenoble)
- Subjects :
- Mathematics - Algebraic Geometry
14M15, 53A20, 53D10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.19376
- Document Type :
- Working Paper