论文标题
与孤立的共同体学上的P^n排列两个捆绑
Rank two bundles on P^n with isolated cohomology
论文作者
论文摘要
本文的目的是研究与$ \ Mathbb p^n $上的第二个矢量捆绑$ \ Mathcal e $相关的最低限度的单子。特别是，我们研究了$ \ Mathcal E $具有$ h^i _*（\ Mathcal e）= 0 $的情况，对于$ 1 <i <n-1 $，除了一对值$（k，n-k）$。我们表明，在$ \ Mathbb p^8，如果$ h^3 _*（\ mathcal e）= h^4 _*（\ mathcal e）= 0 $，则$ \ mathcal e $必须分解。更笼统地，我们表明，对于$ n \ geq 4k $，没有$ h^1_*，h^k_*，h^k_*，h^{n-k} _*，h^{n-k} _*，h^{n-1} _*$为零。
The purpose of this paper is to study minimal monads associated to a rank two vector bundle $\mathcal E$ on $\mathbb P^n$. In particular, we study situations where $\mathcal E$ has $H^i_*(\mathcal E) =0$ for $1<i<n-1$, except for one pair of values $(k,n-k)$. We show that on $\mathbb P^8,$ if $H^3_*(\mathcal E)=H^4_*(\mathcal E)=0$, then $\mathcal E$ must be decomposable. More generally, we show that for $n\geq 4k$, there is no indecomposable bundle $\mathcal E$ for which all intermediate cohomology modules except for $H^1_*, H^k_*, H^{n-k}_*, H^{n-1}_*$ are zero.
