Classification of unstable quartic plane curves
Classification of unstable quartic plane curves
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不稳定四次平面曲线的分类
DOI：
10.1007/s40590-022-00477-w
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Juan Vásquez Aquino
中科院分区：
文献类型：
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作者：
Claudia R. Alcántara;Juan Vásquez Aquino
考虑四次平面曲线空间中坐标变化的作用。我们通过不可约的光滑的局部闭子簇分层对该作用的不稳定点进行了分类。具体地说，我们证明了这些变量参数化了具有特定奇异点的四次平面曲线，并计算了它们的维数和闭包。此外，我们还证明了不稳定点空间由两个不可约分量组成，这两个不可约分量是两个地层的闭合。
Consider the action by change of coordinates in the space of quartic plane curves. We classify the unstable points of this action through a stratification by irreducible, smooth and locally closed subvarieties. Concretely, we show that these varieties parametrize quartic plane curves with specific singularities, we compute their dimensions and closure. In addition, we show that the space of unstable points consists of two irreducible components which are the closure of two of the strata.