全纯Legendrian奇点的刚性性质

IF 0.9 Q2 MATHEMATICS
Jun-Muk Hwang
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引用次数: 1

摘要

研究了接触流形在复解析范畴的Legendrian子变种的奇异性,并证明了两个刚性结果。第一个是具有约切锥的Legendrian奇点与它们的切锥是接触形态生物全纯的。这一结果部分是由范诺接触流形的问题引起的。第二个结果是正规Legendrian奇点的变形刚性,这意味着任何正规Legendrian奇点的全纯族都是平凡的,直到细菌的接触全纯。利用接触流形上的无穷小接触纯态与自然线束的全纯截面之间的关系证明了这两个结果。评论:21页,小修改
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Rigidity properties of holomorphic Legendrian singularities
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. Comment: 21 pages, minor revision
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
19
审稿时长
25 weeks
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