Jun-Muk Hwang - Rigidity properties of holomorphic Legendrian singularities

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

Authors: 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
Published on: December 5, 2019
Submitted on: May 10, 2018
Keywords: Mathematics - Algebraic Geometry,Mathematics - Differential Geometry,58K40, 58K60, 53D10, 14B07


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