论文标题
奇异的接触品种
Singular contact varieties
论文作者
论文摘要
在本说明中，我们提出了在歧管（平滑品种）上对具有理性象图的品种的概念的概括，并证明了此类对象的基本特性。奇异接触品种的自然例子来自尼尔氏轨道的理论：在半神经谎言中，nilpotent轨道闭合的每个项目化都可以在归一化后满足我们的定义。我们显示了与$ \ mathbb {c}^*$ - 捆绑包的结构与触点的结构以及分层的存在之间的对应关系。在揭示的情况下，我们证明了奇异性的奇异和接触分辨率之间的等效性，显示了不释放性并在维度3中对投射接触品种进行完整分类。
In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular contact varieties come from the theory of nilpotent orbits: every projectivization of the closure of a nilpotent orbit in a semisimple Lie algebra satisfies our definition after normalization. We show the correspondence between symplectic varieties with the structure of a $\mathbb{C}^*$-bundle and the contact ones along with the existence of the stratification à la Kaledin. In the projective case we demonstrate the equivalence between crepant and contact resolutions of singularities, show the uniruledness and give a full classification of projective contact varieties in dimension 3.
