论文标题
完整四边形空间的概括
A generalization of the space of complete quadrics
论文作者
论文摘要
对于任何均质的多项式$ h $，我们自然会将各种$ω_h$关联到渐变图$ \ nabla h $的图$γ_h$上，并且当$ h $的空间是通用对称矩阵的确定性时，它与完整四边形的空间一致。我们给出一个足够的标准，即$ω_h$是平滑的，例如，当$ h $是基本对称的多项式时，它适用。在这种情况下，$ω_h$是与某个广义置换体相关的光滑的复曲面品种。当$ω_h$不流畅时，我们还提供了示例。
To any homogeneous polynomial $h$ we naturally associate a variety $Ω_h$ which maps birationally onto the graph $Γ_h$ of the gradient map $\nabla h$ and which agrees with the space of complete quadrics when $h$ is the determinant of the generic symmetric matrix. We give a sufficient criterion for $Ω_h$ being smooth which applies for example when $h$ is an elementary symmetric polynomial. In this case $Ω_h$ is a smooth toric variety associated to a certain generalized permutohedron. We also give examples when $Ω_h$ is not smooth.
