全纯勒让德奇点的刚性性质
Rigidity properties of holomorphic Legendrian singularities
AI总结：
本文在复解析范畴中研究接触流形的勒让德奇点，证明了约化切锥奇点与切锥的接触同胚双全纯等价性，以及正规勒让德奇点的形变刚性，方法基于无穷小接触同胚与自然线丛截面的联系。
摘要：
我们在复解析范畴中研究接触流形的勒让德子簇的奇点，并证明两个刚性结果。第一个结果是，具有约化切锥的勒让德奇点在接触同胚双全纯意义下与其切锥同构。该结果部分受法诺接触流形上的一个问题的启发。第二个结果是正规勒让德奇点的形变刚性，即任何正规勒让德奇点的全纯族在芽的接触同胚双全纯意义下都是平凡的。两个结果均通过利用无穷小接触同胚与接触流形上自然线丛的全纯截面之间的关系来证明。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
