光滑Quot概型的分类
Classifying Smooth Quot Schemes
浏览论文内容
中文总结 AI 辅助
本研究针对n维射影空间上的$\text{Quot}$概型$\text{Quot}^{q}(\text{O}_{\text{P}^n}^{r})$，确定多项式q的数值条件以判定其光滑性与不可约性，同时揭示了该概型字典序点的光滑性等几何特征。
中文摘要 AI 辅助
Quot概型$\boldsymbol{\text{Quot}}^{q}(\boldsymbol{\text{O}}_{\boldsymbol{\text{P}}^n}^{r})$参数化n维射影空间上秩为r的平凡向量丛、具有希尔伯特多项式q且在基概型上平坦的商层。我们确定多项式q的数值条件，完全判定该Quot概型何时光滑且不可约；该方法还揭示了$\boldsymbol{\text{Quot}}^{q}(\boldsymbol{\text{O}}_{\boldsymbol{\text{P}}^n}^{r})$射影概型的更多几何特征，包括字典序点的光滑性。
英文摘要
The Quot scheme $\operatorname{Quot}^{q}(\mathcal{O}_{\mathbb{P}^n}^{r})$ parametrizes the quotients of the trivial vector bundle of rank $r$ on $n$-dimensional projective space that have Hilbert polynomial $q$ and are flat over a base scheme. We identify numerical conditions on the polynomial $q$ that completely determine when this Quot scheme is smooth and irreducible. Our approach also uncovers further geometric features of the projective scheme $\operatorname{Quot}^{q} (\mathcal{O}_{\mathbb{P}^n}^{r})$ including the smoothness of the lexicographic point.
