论文标题
递归曲线的递归公式
A Recursive Formula for Osculating Curves
论文作者
论文摘要
令$ x $为平滑的复杂投影品种。使用为Gathmann设计的建筑，我们为$ x $的某些Gromov-witten不变性人士提供了递归公式。我们证明，当$ x $均匀时，此公式在$ x $的一般性高表面的一般点提供了示波的理性曲线数量。这概括了鲑鱼的$ \ mathbb {p}^{3} $中的表面的经典反弹对（渐近）线，以及Darboux的$ 27 $ osculating Conics。
Let $X$ be a smooth complex projective variety. Using a construction devised to Gathmann, we present a recursive formula for some of the Gromov-Witten invariants of $X$. We prove that, when $X$ is homogeneous, this formula gives the number of osculating rational curves at a general point of a general hypersurface of $X$. This generalizes the classical well known pairs of inflexion (asymptotic) lines for surfaces in $\mathbb{P}^{3}$ of Salmon, as well as Darboux's $27$ osculating conics.
