论文标题
来自Hypersurfaces上点配置的确定品种
Determinantal varieties from point configurations on hypersurfaces
论文作者
论文摘要
我们考虑该方案$ x_ {r，d，n} $参数化$ n $ dround在投射空间中订购点$ \ mathbb {p}^r $，该点位于$ d $的公共hypersurface上。我们表明该方案具有确定性结构，我们证明它是不可约，Cohen-Macaulay和正常的。此外，我们对Castelnuovo-Mumford的规律性和$ d $ normality进行了$ x_ {r，d，n} $的单数基因座的代数和几何描述。这产生了$ x_ {2，d，n} $和$ x_ {3,2，n} $的奇异基因座的表征。
We consider the scheme $X_{r,d,n}$ parametrizing $n$ ordered points in projective space $\mathbb{P}^r$ that lie on a common hypersurface of degree $d$. We show that this scheme has a determinantal structure and we prove that it is irreducible, Cohen-Macaulay, and normal. Moreover, we give an algebraic and geometric description of the singular locus of $X_{r,d,n}$ in terms of Castelnuovo-Mumford regularity and $d$-normality. This yields a characterization of the singular locus of $X_{2,d,n}$ and $X_{3,2,n}$.
