近似曲线的递推公式

IF 0.8 4区数学 Q2 MATHEMATICS

Arkiv for Matematik Pub Date : 2020-02-28 DOI:10.1307/mmj/20216025

G. Muratore

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引用次数: 4

摘要

设$X$为光滑复射影变量。利用Gathmann的构造，我们给出了X的一些Gromov-Witten不变量的递归公式。证明了当$X$为齐次时，该公式给出了$X$的一般超曲面的一般点处的密切有理曲线的个数。这推广了Salmon的$\mathbb{P}^{3}$中曲面的经典拐点(渐近)线对，以及Darboux的$27$密切曲线。

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A recursive formula for osculating curves

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.

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来源期刊

Arkiv for Matematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishing research papers, of short to moderate length, in all fields of mathematics.