论文标题
传奇叶子的列举几何形状：接触的故事
Enumerative geometry of Legendrian foliations: a Tale of Contact
论文作者
论文摘要
射影三空间上的联系分布由1型$ x_2dx_1-x_1dx_2+x_4dx_3-x_3dx_4 $定义，最多可以更改投影坐标。 pfaff-plückerQuadric的补充在反对称$ 4 \ times4 $矩阵中的pfaff-plückerQuadric的补充进行了参数化。多项式向量字段$ \ sum {} p_i \ partial_ {x_i}，p_i $同质度$ d $。如果与某种接触分布相切，则称为Legendrian。我们的目标是为legendrian叶子的各种尺寸和程度提供公式，以及与飞机铅笔相切的叶子变种的公式。
A contact distribution on projective three-space is defined by the 1-form $x_2dx_1-x_1dx_2+x_4dx_3-x_3dx_4$, up to a change of projective coordinates. The family of contact distributions is parameterized by the complement of the Pfaff-Plücker quadric in the projective 5-space of antisymmetric $4\times4$ matrices. A foliation of dimension 1 and degree $d$ is specified by a polynomial vector field $\sum{}p_i\partial_{x_i}, p_i$ homogeneous of degree $d$. The foliation is called Legendrian if tangent to some distribution of contact. Our goal is to give formulas for the dimensions and degrees of the varieties of Legendrian foliations, and of the varieties of foliations tangent to a pencil of planes.
