Characterizing subadjoint varieties among Legendrian varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911860025982976 |
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| author | Hwang, Jun-Muk |
| author_facet | Hwang, Jun-Muk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19376 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing subadjoint varieties among Legendrian varieties Hwang, Jun-Muk Algebraic Geometry 14M15, 53A20, 53D10 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. |
| title | Characterizing subadjoint varieties among Legendrian varieties |
| topic | Algebraic Geometry 14M15, 53A20, 53D10 |
| url | https://arxiv.org/abs/2404.19376 |