接触歧管上的线路II
Lines on contact manifolds II
摘要：
复切触流形最近受到了相当大的关注。许多较新的出版物方法接触流形通过覆盖家庭的最小有理曲线。这篇短文进一步研究了这些曲线。已知对于X中的任何点x，由包含x的那些曲线覆盖的子簇是勒让德的。现在我们将研究通过移动基点产生的这些子簇的变形。作为一个主要应用，我们对J.M. Hwang在切触流形的情形中：一个充分一般的切向量至多包含在一条极小有理曲线中。作者认为这是对切触流形进行完全分类的必要步骤。我们给出了第二个应用表明，通过X的最小曲线的子品种的正规化是同构的投影锥。
英文摘要：
Complex contact manifolds have recently received considerable attention. Many of the newer publications approach contact manifolds via the covering family of minimal rational curves. This short note furthers the study of these curves. It is known that for any point x in X, the subvariety, which is covered by those curves which contain x, is Legendrian. We will now study the deformations of these subvarieties which are generated by moving the base point. As a main application, we give a positive answer to a question of J.M. Hwang in the case of contact manifolds: a sufficiently general tangent vector is contained in at most a single minimal rational curve. The author believes that this is a necessary step towards a full classification of contact manifolds. We give a second application by showing that the normalization of the subvariety of minimal curves through x is isomorphic to a projective cone.
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。
