Jun-Muk Hwang - Rigidity properties of holomorphic Legendrian singularities

epiga:4495 - Épijournal de Géométrie Algébrique, 5 décembre 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.4495
Rigidity properties of holomorphic Legendrian singularitiesArticle

Auteurs : Jun-Muk Hwang

    We study the singularities of Legendrian subvarieties of contact manifolds in the complex-analytic category and prove two rigidity results. The first one is that Legendrian singularities with reduced tangent cones are contactomorphically biholomorphic to their tangent cones. This result is partly motivated by a problem on Fano contact manifolds. The second result is the deformation-rigidity of normal Legendrian singularities, meaning that any holomorphic family of normal Legendrian singularities is trivial, up to contactomorphic biholomorphisms of germs. Both results are proved by exploiting the relation between infinitesimal contactomorphisms and holomorphic sections of the natural line bundle on the contact manifold.


    Volume : Volume 3
    Publié le : 5 décembre 2019
    Accepté le : 25 octobre 2019
    Soumis le : 10 mai 2018
    Mots-clés : Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,58K40, 58K60, 53D10, 14B07

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