论文标题
关于希尔伯特方案上词素点的平稳性
On the smoothness of lexicographic points on Hilbert schemes
论文作者
论文摘要
我们研究多项式环和外部代数的标准分级希尔伯特方案的几何形状。我们的调查是由著名的里夫斯（Reeves）和斯蒂尔曼（Stillman）的著名定理进行的，该定理的Grothendieck Hilbert计划指出，该计划的词典学位很顺利。相比之下，我们表明，在多项式环和外部代数的标准分级希尔伯特方案中，词典学点可能是单数的，并且可以在多个不可减少的组件中。我们回答了Peeva-Stillman和Maclagan-Smith的问题。
We study the geometry of standard graded Hilbert schemes of polynomial rings and exterior algebras. Our investigation is motivated by a famous theorem of Reeves and Stillman for the Grothendieck Hilbert scheme, which states that the lexicographic point is smooth. By contrast, we show that, in standard graded Hilbert schemes of polynomial rings and exterior algebras, the lexicographic point can be singular, and it can lie in multiple irreducible components. We answer questions of Peeva-Stillman and of Maclagan-Smith.
