论文标题
四曲线的特殊几何形状
Special geometry of quartic curves
论文作者
论文摘要
我们将最大四分之一的广义投射特殊真实曲线分类为等效性。最大的四分之一广义的投影特殊真实曲线由连接的组成部分组成，这是四分之一同质的真实多项式$ H：\ Mathbb {r}^2 \ to \ Mathbb {r} $及其级别设置$ \ \ {H = 1 \ \} $。如果两个这样的曲线通过线性坐标转换相关，则称为等效曲线。作为我们结果的应用，我们证明，与均质空间的四分之一广义的投影特殊的真实歧管具有非规范的边界行为，这意味着，这些空间的定义多项式的差异在锥形的边界上的射线上相同消失。最后，我们描述了每条曲线的渐近行为。
We classify maximal quartic generalised projective special real curves up to equivalence. A maximal quartic generalised projective special real curve consists of connected components of the intersection of the hyperbolic points of a quartic homogeneous real polynomial $h:\mathbb{R}^2\to\mathbb{R}$ and its level set $\{h=1\}$. Two such curves are called equivalent if they are related by a linear coordinate transformation. As an application of our results we prove that quartic generalised projective special real manifolds that are homogeneous spaces have non-regular boundary behaviour, meaning that the differential of each of these spaces' defining polynomials vanishes identically on a ray in the boundary of the cone spanned by the corresponding manifold. Lastly we describe the asymptotic behaviour of each curve.
