论文标题
较高等级除数和某些希尔伯特计划的对角特性和弱点特性
Diagonal property and weak point property of higher rank divisors and certain Hilbert schemes
论文作者
论文摘要
在本文中，我们介绍了对角性质的概念和弱点特性的索引。我们证明，在光滑的投影曲线上，积分斜率较高等级的索引具有弱点属性。此外，我们表明$（1，n）$ - 除数具有对角线属性。此外，我们获得了与恒定多项式的良好分区相关的希尔伯特方案满足对角线特性。在获得此过程的过程中，我们在此类希尔伯特方案的数量上为同构提供了上限。此外，我们证明在零曲线属的情况下，获得的上限是达到的，因此得出结论是锋利的。
In this paper, we introduce the notion of the diagonal property and the weak point property for an ind-variety. We prove that the ind-varieties of higher rank divisors of integral slopes on a smooth projective curve have the weak point property. Moreover, we show that the ind-variety of $(1,n)$-divisors has the diagonal property. Furthermore, we obtain that the Hilbert schemes associated to the good partitions of a constant polynomial satisfy the diagonal property. On the process of obtaining this, we provide an upper bound on the number of such Hilbert schemes up to isomorphism. Furthermore, we prove that the obtained upper bound is attained in case of genus zero curves and hence conclude that the bound is sharp.
