论文标题
在限制配置空间的极限消失
On the limiting extremal vanishing for configuration spaces
论文作者
论文摘要
我们研究了$ k $ - 点配置的极端同胞组的局限性行为，该配置的配置空间是复杂维度的复杂射击空间$ m \ geq 4. $在先前的工作中，我们证明，极端学位$（2M-2）K+i $的极端共同体群体最终对每个$ i \ in \ in \ in \ in \ in \ in \ in \ {1,2,3,3 \} $ con is proump comply of com}。非阳性整数，并表明这些共同体组最终以$ i \ in \ { - 1，-2,0 \}的$ i \作为一种应用程序而消失，我们确认了Knudsen，Miller和Tosteson更一般性问题的有效性。我们为某些不稳定的共同学团体的家庭提供了最终并没有消失的家庭。这些共同体学群体家族的程度取决于点的数量和射影空间的维度。我们提出了这样一种猜想，即较高坡度的同一个群体最终消失了。
We study the limiting behavior of extremal cohomology groups of $k$-points configuration spaces of complex projective spaces of complex dimension $m\geq 4.$ In the previous work, we prove that the extremal cohomology groups of degrees $(2m-2)k+i$ are eventually vanish for each $i\in\{1,2,3\}.$ In this paper, we investigate the extremal cohomology groups for non-positive integers, and show that these cohomology groups are eventually vanish for $i\in\{-1,-2,0\}.$ As an application, we confirm the validity of more general question of Knudsen, Miller and Tosteson for non-positive integers. We give a certain families of unstable cohomology groups, which are not eventually vanish. The degrees of these families of cohomology groups are depend on the number of points and the dimension of projective spaces. We formulate the conjecture that the cohomology groups of higher slopes are eventually vanish.
